161.
Coloured peak algebras and Hopf algebras
- Bergeron, Nantel; Hohlweg, Christophe
For $G$ a finite abelian group, we study the properties of general
equivalence relations on $G_n=G^n\rtimes \SG_n$, the wreath product of $G$ with
the symmetric group $\SG_n$, also known as the $G$-coloured symmetric group. We
show that under certain conditions, some equivalence relations give rise to
subalgebras of $\k G_n$ as well as graded connected Hopf subalgebras of
$\bigoplus_{n\ge o} \k G_n$. In particular we construct a $G$-coloured peak
subalgebra of the Mantaci-Reutenauer algebra (or $G$-coloured descent algebra).
We show that the direct sum of the $G$-coloured peak algebras is a Hopf
algebra. We also have similar results for a $G$-colouring of the Loday-Ronco
Hopf algebras of planar binary...
162.
Duality and Operator Algebras II: Operator Algebras as Banach Algebras
- Blecher, David P.; Magajna, Bojan
We answer, by counterexample, several open questions concerning algebras of
operators on a Hilbert space. The answers add further weight to the thesis
that, for many purposes, such algebras ought to be studied in the framework of
operator spaces, as opposed to that of Banach spaces and Banach algebras. In
particular, the `nonselfadjoint analogue' of a W*-algebra resides naturally in
the category of dual operator spaces, as opposed to dual Banach spaces. We also
show that an automatic w*-continuity result in the preceding paper of the
authors is sharp.
163.
A Process Algebra with Distributed Priorities
- R. Cleaveland; G. Lüttgen; V. Natarajan
This paper presents a process algebra for distributed systems in which some actions may take precedence over others. In contrast with existing approaches to priorities, our algebra only allows actions to take priority over others at the same "location" and therefore captures a notion of localized preemption. Using Park's and Milner's notion of strong bisimulation as a basis, we develop a behavioral congruence and axiomatize it for finite processes; we also derive an associated observational congruence. Simple examples are given that highlight the utility of the theory. Keywords: process algebras, distributed systems, priorities, bisimulation, localized preemption, locations, axiomatization. Research supported...
164.
Generalized Vertex Algebras
- Bakalov, Bojko; Kac, Victor G.
We give a short introduction to generalized vertex algebras, using the notion
of polylocal fields. We construct a generalized vertex algebra associated to a
vector space h with a symmetric bilinear form. It contains as subalgebras all
lattice vertex algebras of rank equal to dim h and all irreducible
representations of these vertex algebras.
165.
The Jacobian algebras
- Bavula, V. V.
The Jacobian algebras are introduced and their various properties are
studied.
166.
Novikov-Jordan algebras
- Dzhumadil'daev, A. S.
Algebras with identity $(a\star b)\star (c\star d) -(a\star d)\star(c\star
b)$ $=(a,b,c)\star d-(a,d,c)\star b$ are studied. Novikov algebras under Jordan
multiplication and Leibniz dual algebras satisfy this identity. If algebra with
such identity has unit, then it is associative and commutative.
167.
Ideals in Toeplitz Algebras
- Douglas, Ronald G.
We determine the ideal structure of the Toeplitz C*-algebra on the bidisk.
168.
Twisted Quantum Affine Algebras
- Chari, Vyjayanthi; Pressley, Andrew
We classify the irreducible finite-dimensional representations of the twisted
quantum affine algebras.
169.
Non-separable AF-algebras
- Katsura, Takeshi
We give two pathological phenomena for non-separable AF-algebras which do not
occur for separable AF-algebras. One is that non-separable AF-algebras are not
determined by their Bratteli diagrams, and the other is that there exists a
non-separable AF-algebra which is prime but not primitive.
170.
Tópicos de álgebras alternativas
- Marcos Munhoz
São estudados alguns aspectos das álgebras alternativas, como o bar-radical de uma álgebra bárica alternativa e as identidades de grau 4 e 5 nas álgebras de Cayley-Dickson. Neste estudo fazemos uso da decomposição de Peirce e de diversas propriedades importantes das álgebras alternativas. Concluímos mostrando que as únicas identidades de grau 4 são as triviais e as de grau 5 são conseqüência de outras duas identidades conhecidas
171.
A Process Algebra with Distributed Priorities
- R. Cleaveland; G. Lüttgen; V. Natarajan
This paper presents a process algebra for distributed systems in which some actions may take precedence over others. In contrast with existing approaches to priorities, our algebra only allows actions to take priority over others at the same "location" and therefore captures a notion of localized preemption. Using Park's and Milner's notion of strong bisimulation as a basis, we develop a behavioral congruence and axiomatize it for finite processes; we also derive an associated observational congruence. Simple examples are given that highlight the utility of the theory.
172.
Generalized quantum current algebras
- Zhao, Liu
Two general families of new quantum deformed current algebras are proposed
and identified both as infinite Hopf family of algebras, a structure which
enable one to define ``tensor products'' of these algebras. The standard
quantum affine algebras turn out to be a very special case of both algebra
families, in which case the infinite Hopf family structure degenerates into
standard Hopf algebras. The relationship between the two algebra families as
well as their various special examples are discussed, and the free boson
representation is also considered.
173.
H_T Vertex Algebras
- Bergvelt, Maarten J
The usual vertex algebras have as underlying symmetry the Hopf algebra
$H_D=\mathbb C[D]$ of infinitesimal translations. We show that it is possible
to replace $H_D$ by another symmetry algebra $H_T=\mathbb C[T,T\inv]$, the
group algebra of the Abelian group generated by $T$. $H_T$ is the algebra of
symmetries of a lattice of rank 1, and the construction gives a class of vertex
algebras related to the Infinite Toda Lattice in the same way as the usual
$H_D$-vertex algebras are related to Korteweg-de Vries hierarchies.
174.
Generalising Group Algebras
- Grundling, Hendrik
We generalise group algebras to algebraic objects with bounded Hilbert space
representation theory - the generalised group algebras are called "host"
algebras. The main property of a host algebra, is that its representation
theory should be isomorphic (in the sense of the Gelfand--Raikov theorem) to a
specified subset of representations of the algebraic object. Here we obtain
both existence and uniqueness theorems for host algebras as well as general
structure theorems for host algebras. Abstractly, this solves the question of
when a set of Hilbert space representations is isomorphic to the representation
theory of a C*-algebra. To make contact with harmonic analysis, we consider
general convolution algebras associated to...
175.
Minimal Resolutions of Algebras
. A method is described for constructing the minimal projective resolution
of an algebra considered as a bimodule over itself. The method applies to an
algebra presented as the quotient of a tensor algebra over a separable algebra
by an ideal of relations which is either homogeneous or admissable (with some
additional finiteness restrictions in the latter case). In particular, it applies to
any finite dimensional algebra over an algebraically closed field. The method is
illustrated by a number of examples, viz. truncated algebras, monomial algebras
and Koszul algebras, with the aim of unifying existing treatments of these in the
literature.
1991 Mathematics Subject Classification. Primary: 16E99, 18G10. Secondary:
16D20,...
176.
Hopf algebras of endomorphisms of Hopf algebras
- Hazewinkel, Michiel
In the last decennia two generalizations of the Hopf algebra of symmetric
functions have appeared and shown themselves important, the Hopf algebra of
noncommutative symmetric functions NSymm and the Hopf algebra of quasisymmetric
functions QSymm. It has also become clear that it is important to understand
the noncommutative versions of such important structures as Symm the Hopf
algebra of symmetric functions. Not least because the right noncommmutative
versions are often more beautiful than the commutaive ones (not all cluttered
up with counting coefficients). NSymm and QSymm are not truly the full
noncommutative generalizations. One is maximally noncommutative but
cocommutative, the other is maximally non cocommutative but commutative. There
is a...
177.
On FRT-Clifford Algebras
- Heckenberger, I.; Schueler, A.
We study the q-Clifford algebras Cl_q(N,c), called FRT-Clifford algebras,
introduced by Faddeev, Reshetikhin and Takhtajan. It is shown that Cl_q(N,c)
acts on the q-exterior algebra \Lambda(O_q^N). Moreover, explicit formulas for
the embedding of U_q(so_N) into Cl_q(N,c) and its relation to the vector and
spin representations of U_q(so_N) are given and proved.
Key Words: q-Clifford algebra, Drinfeld-Jimbo algebra, spin representation
178.
Hopf C*-algebras
- Vaes, Stefaan; Van Daele, Alfons
In this paper we introduce the notion of a Hopf C*-algebra and construct the
counit and antipode. A Hopf C*-algebra is a C*-algebra with comultiplication
satisfying some extra condition which makes possible the construction of the
counit and antipode. The leading example is of course the C*-algebra of
continuous, vanishing at infinity functions on a locally compact group. Also
locally compact quantum groups will be examples. We include several formulas
for the counit and antipode which are familiar from Hopf algebra theory.
179.
Indecomposable representations of generalized Weyl algebras
- Vladimir Bavula; Viktor Bekkert; Let An Algebra A
For a class of generalized Weyl algebras which includes the Weyl algebras A n the tame criteria is given for the problem of describing indecomposable weight and generalized weight modules with supports from a fixed orbit. In tame cases all the indecomposable modules are described. Introduction Let an algebra A =\Omega n 1 A i be the tensor product over an algebraically closed field K of generalized Weyl algebras A i = D i (oe i ; a i ) of degree 1 (see subsec. 1.1 and 1.4) with basic polynomial rings D i = K[H i ] in one...
180.
Shape Groups For C*-Algebras
- Zvonko Cerin
: We shall describe in this paper shape groups for C -algebras and prove some of their basic properties. 1. Introduction In the paper [5] the author has defined homotopy groups for C - algebras. More precisely, we have described how to associate with every pair (A; B) of C -algebras and every integer n 0 pointed sets ßn (A; B) for n = 0 and groups ßn (A; B) for n 1 which are commutative for n 2, which depend only on homotopy types of A and B, and which have other properties similar to the properties of absolute...
