181.
Vertex operator algebras and associative algebras
- Dong, Chongying; Li, Haisheng; Mason, Geoffrey
Let V be a vertex operator algebra. We construct a sequence of associative
algebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V)
and a pair of functors between the category of A_n(V)-modules which are not
A_{n-1}(V)-modules and the category of admissible V-modules. These functors
exhibit a bijection between the simple modules in each category. We also show
that V is rational if and only if all A_n(V) are finite-dimensional semisimple
algebras.
182.
Homotopy Gerstenhaber algebras
- Voronov, Alexander A.
The purpose of this paper is to complete Getzler-Jones' proof of Deligne's
Conjecture, thereby establishing an explicit relationship between the geometry
of configurations of points in the plane and the Hochschild complex of an
associative algebra. More concretely, it is shown that the B_infty-operad,
which is generated by multilinear operations known to act on the Hochschild
complex, is a quotient of a certain operad associated to the compactified
configuration spaces. Different notions of homotopy Gerstenhaber algebras are
discussed: one of them is a B_infty-algebra, another, called a homotopy
G-algebra, is a particular case of a B_infty-algebra, the others, a
G_infty-algebra, an E^1-bar-algebra, and a weak G_infty-algebra, arise from the
geometry...
183.
Quantized Algebras of Functions on Affine Hecke Algebras
- Diep, Do Ngoc
The so called quantized algebras of functions on affine Hecke algebras of
type A and the corresponding q-Schur algebras are defined and their irreducible
unitarizable representations are classified.
184.
A restriction algebra related to Fourier algebras
this paper we consider the Fourier algebra A(R
), Fourier transformation
F : ' 7! b ' for ' 2 L
) being defined by
b '(y) =
'(x) dx ; (1)
where, in the usual way, for x = (x 1 ; x 2 ), y = (y 1 ; y 2 ) we write x Delta y = x 1 y 1 + x 2 y 2 and
jxj =
x Delta x. The injectivity of F implies that by k b 'k A(R
) = k'k 1 a norm is defined on A(R
),
and in this way A(R
), equipped with pointwise multiplication and complex conjugation, is
made into...
185.
Relation algebra reducts of cylindric algebras and complete representations
- Hirsch, Robin
We show, for any ordinal ? ? 3, that the class
???CA
? is pseudo-elementary and has a recursively enumerable
elementary theory. S
cK denotes the class of strong
subalgebras of members of the class K. We devise games, F
n
(3? n??), G, H, and show, for an atomic relation algebra
?? with countably many atoms, that
[start-list]
*
? has a winning strategy in
F
?(At(??))?
???S
c???CA
?,
*? has a winning strategy in F
n(At(??))
? ???S
c???CA
n,
*? has a winning strategy in
G(At(??)) ? ??????CA
?,
*? has a winning strategy in
H(At(??))???????RCA
?[end-list]
for 3? n < ?.
We use these games to show, for ?? 5 and any class K of
relation algebras satisfying
¶
???RCA
? ? K
? S
c???CA
5,
¶
that K is not
closed under...
186.
Semiquasitriangular Hopf algebras
- Guccione, Jorge A.; Guccione, Juan J.
We say that a Hopf algebra H is semicocommutative if the right adjoint
coaction factorizes through the tensor product of H with the center of H. For
instance the commutative and the cocommutative Hopf algebras are
semicocommutative. The quasitriangular Hopf algebras generalize the
cocommutative Hopf algebras. In this paper we introduce and begin the study of
a similar generalization for the semicocommutative ones. These algebras, which
we call semiquasitriangular Hopf algebras have many of the basic properties of
the quasitriangular ones. In particular, they have associated braided
categories of representations in a natural way.
187.
Abelianizing vertex algebras
- Li, Haisheng
To every vertex algebra $V$ we associate a canonical decreasing sequence of
subspaces and prove that the associated graded vector space $gr(V)$ is
naturally a vertex Poisson algebra, in particular a commutative vertex algebra.
We establish a relation between this sequence and the sequence $C_{n}$
introduced by Zhu. By using the (classical) algebra $gr(V)$, we prove that for
any vertex algebra $V$, $C_{2}$-cofiniteness implies $C_{n}$-cofiniteness for
all $n\ge 2$. We further use $gr(V)$ to study generating subspaces of certain
types for lower truncated $Z$-graded vertex algebras.
188.
$W^{(2)}_n$ algebras
- Feigin, BL; Semikhatov, AM
We construct W-algebra generalizations of the ^sl(2) algebra -- W-algebras
W^{(2)}_n generated by two currents E and F with the highest pole of order n in
their OPE. The n=3 term in this series is the Bershadsky--Polyakov algebra. We
define these algebras as a centralizer (commutant) of the $U_{q}sl(n|1)$ super
quantum group and explicitly find the generators in a factored, ``Miura-like''
form. Another construction of W^{(2)}_n is in terms of the coset
^sl(n|1)/^sl(n). The relation between the two constructions involves the
``duality'' (k+n-1)(k'+n-1)=1 between levels k and k' of two ^sl(n) algebras.
189.
Automorphisms of Regular Algebras
- Popov, Todor
Manin associated to a quadratic algebra (quantum space) the quantum matrix
group of its automorphisms. This Talk aims to demonstrate that Manin's
construction can be extended for quantum spaces which are non-quadratic
homogeneous algebras. Here given a regular Artin-Schelter algebra of dimension
3 we construct the quantum group of its symmetries, i.e., the Hopf algebra of
its automorphisms. For quadratic Artin-Schelter algebras these quantum groups
are contained in the the classification of the GL(3) quantum matrix groups due
to Ewen and Ogievetsky. For cubic Artin-Schelter algebras we obtain new quantum
groups which are automorphisms of cubic quantum spaces.
190.
Hammocks for String Algebras
this paper we consider the class of string algebras and deal with the corresponding
problem. These algebras are usually representation-infinite and
are regarded as an important class of tame algebras. We introduce a generalized
notion of hammocks for string algebras and prove various combinatorial
properties of these posets. In case one is dealing with a representation-finite
string algebra, our definition and the definition given in [RV] coincide.
As a main application we compute the index of nilpotency (up to a small
error term) of the radical of A-mod where A is a string algebra. We also
construct examples which show that every possible index occurs. Only very
few examples...
191.
Non-trivial derivations on commutative regular algebras
- Ber, A.F.; Chilin, V.I.; Sukochev, F.A.
Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all Lebesgue measurable functions on [0,1], our results imply that the first (Hochschild) cohomology group H1(S[0,1], S[0,1]) is non-trivial.
192.
General Algebras
- Yvind B. Fredriksen
We study categories of algebras (for a given signature) constructed
from arbitrary categories C with specific finite products. We show how
a left adjoint Set - C may be utilized to construct an initial algebra
satisfying a given set of equations. Finally, we give a condition under which
satisfaction of equations is independent of the set of variables considered.
1 Introduction
This paper reports work in progress. It is concerned with specifications of
abstract data types and in particular with the semantics of such specifications.
Here we will only consider one-sorted equational specifications or presentations,
having two parts:
ffl the names (called operation symbols) of the operations involved, together
with their...
193.
General Algebras
- Yvind B. Fredriksen
We study categories of algebras (for a given signature) constructed
from arbitrary categories C with specific finite products. We show how
a left adjoint Set - C may be utilized to construct an initial algebra
satisfying a given set of equations. Finally, we give a condition under which
satisfaction of equations is independent of the set of variables considered.
1 Introduction
This paper reports work in progress. It is concerned with specifications of
abstract data types and in particular with the semantics of such specifications.
Here we will only consider one-sorted equational specifications or presentations,
having two parts:
ffl the names (called operation symbols) of the operations involved, together
with their...
194.
General Algebras
- Yvind B. Fredriksen
We study categories of algebras (for a given signature) constructed
from arbitrary categories C with specific finite products. We show how
a left adjoint Set - C may be utilized to construct an initial algebra
satisfying a given set of equations. Finally, we give a condition under which
satisfaction of equations is independent of the set of variables considered.
1 Introduction
This paper reports work in progress. It is concerned with specifications of
abstract data types and in particular with the semantics of such specifications.
Here we will only consider one-sorted equational specifications or presentations,
having two parts:
ffl the names (called operation symbols) of the operations involved, together
with their...
195.
Algebras and their Associated Monomial Algebras
- Li, Huishi
Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra
over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be
an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and
the $\Gamma$-filtration $FA$ induced by $FR$ for the quotient $K$-algebra
$A=R/I$, we show that there is a $\Gamma$-graded $K$-algebra isomorphism
$G(A)\cong \bar{A}=R/<\hbox{\bf HT} (I)>$, where $G(A)$ is the associated
$\Gamma$-graded $K$-algebra of $A$ defined by $FA$, and $<\hbox{\bf HT}(I)>$ is
the $\Gamma$-graded ideal of $R$ generated by the set of head terms of $I$. In
the case that $\Gamma$ is an ordered monoid with a well-ordering, this result
enables us to lift many nice structural properties...
196.
Planar algebras, I
- Jones, Vaughan F. R.
We introduce a notion of planar algebra, the simplest example of which is a
vector space of tensors, closed under planar contractions. A planar algebra
with suitable positivity properties produces a finite index subfactor of a II_1
factor, and vice versa.
197.
Quantum Heisenberg--Weyl Algebras
- Ballesteros, Angel; Herranz, Francisco J.; Parashar, Preeti
All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$
are classified and explicitly quantized. The complete list of quantum
Heisenberg--Weyl algebras so obtained includes new multiparameter deformations,
most of them being of the non-coboundary type.
198.
Constructing quantum vertex algebras
- Li, Haisheng
This is a sequel to \cite{li-qva}. In this paper, we focus on the
construction of quantum vertex algebras over $\C$, whose notion was formulated
in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator
algebra (over $\C[[h]]$) as one of the main motivations. As one of the main
steps in constructing quantum vertex algebras, we prove that every
countable-dimensional nonlocal (namely noncommutative) vertex algebra over
$\C$, which either is irreducible or has a basis of PBW type, is nondegenerate
in the sense of Etingof and Kazhdan. Using this result, we establish the
nondegeneracy of better known vertex operator algebras and some nonlocal vertex
algebras. We then construct a...
199.
Algebras with a compatible uniformity
- Rowan, William H.
Given a variety of algebras V, we study categories of algebras in V with a
compatible structure of uniform space. The lattice of compatible uniformities
of an algebra, Unif A, can be considered a generalization of the lattice of
congruences Con A. Mal'cev properties of V influence the structure of Unif A,
much as they do that of Con A. The category V[CHUnif] of complete, Hausdorff
uniform algebras in the variety V is particularly interesting; it has a natural
factorization system extending the usual (onto, one-one) factorization system
of V.
200.
Cosovereign Hopf algebras
- Bichon, Julien
In this paper we define and study the algebraic conterpart of sovereign
monoidal categories : cosovereign Hopf algebras.
