141.
Local Quasitriangular Hopf Algebras
- Zhang, Shouchuan; Gould, Mark D.; Zhang, Yao-Zhong
We find a new class of Hopf algebras, local quasitriangular Hopf algebras,
which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we
obtain solutions of the Yang-Baxter equation in a systematic way. The category
of modules with finite cycles over a local quasitriangular Hopf algebra is a
braided tensor category.
142.
Spectral synthesis in the Fourier algebra and the Varopoulos algebra
- Parthasarathy, Krishnan; Prakash, Rajendran
The objects of study in this paper are sets of spectral synthesis for the Fourier algebra $A(G)$ of a locally compact group and the Varopoulos algebra $V(G)$ of a compact group with respect to submodules of the dual space. Such sets of synthesis are characterized in terms of certain closed ideals. For a closed set in a closed subgroup $H$ of $G,$ the relations between these ideals in the Fourier algebras of $G$ and $H$ are obtained. The injection theorem for such sets of synthesis is then a consequence. For the Fourier algebra of the quotient modulo a compact subgroup,...
143.
Hecke algebras of group extensions
- Baumgartner, Udo. University of Newcastle; Foster, James. University of Newcastle; Hicks, Jacqueline. University of Newcastle; Lindsay, Helen. University of Newcastle; Maloney, Ben. University of Newcastle; Raeburn, Iain. University of Newcastle; Ramagge, Jacqueline. University of Newcastle; Richardson, Sarah
We describe the Hecke algebra H(Gamma,Gamma(0)) of a Hecke pair (Gamma, Gamma(0)) in terms of the Hecke pair (N, Gamma(0)) where N is a normal subgroup of Gamma containing Gamma(0). To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S subset of Gamma/ N satisfies S-1 S = Gamma/N , we show that H(Gamma, Gamma(0)) is the twisted crossed product of (N ,Gamma(0)) by S . This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.
144.
Hecke algebras of group extensions
- Baumgartner, Udo; Foster, James; Hicks, Jacqueline; Lindsay, Helen; Maloney, Ben; Raeburn, Iain; Ramagge, Jacqueline; Richardson, Sarah
We describe the Hecke algebra H(Gamma,Gamma(0)) of a Hecke pair (Gamma, Gamma(0)) in terms of the Hecke pair (N, Gamma(0)) where N is a normal subgroup of Gamma containing Gamma(0). To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S subset of Gamma/ N satisfies S-1 S = Gamma/N , we show that H(Gamma, Gamma(0)) is the twisted crossed product of (N ,Gamma(0)) by S . This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.
145.
Elliptic Hecke algebras and modified Cherednik algebras
- Takebayashi, Tadayoshi
The elliptic Hecke algebras associated to the 1-codimensional
elliptic root systems have been defined by H. Yamada [10],
which are subalgebras of Cherednik's double affine Hecke algebras
[2, 3]. The elliptic Hecke algebras associated to the elliptic
root systems of type $X^{(1,1)}$ have been defined similarly
by the author [11] in terms of generators and relations associated
to the completed elliptic diagram. On the other hand, M. Kapranov
[6] has defined modified Cherednik algebras associated to the
double coset decomposition of the group schemes over 2-dimensional
local field. In this paper, we see that modified Cherednik
algebras are isomorphic to elliptic Hecke algebras of type
$X^{(1,1)}$.
146.
Plethystic algebra
- Borger, James; Wieland, Ben
The notion of a Z-algebra has a non-linear analogue, whose purpose it is to
control operations on commutative rings rather than linear operations on
abelian groups. These plethories can also be considered non-linear
generalizations of cocommutative bialgebras. We establish a number of
category-theoretic facts about plethories and their actions, including a
Tannaka-Krein-style reconstruction theorem. We show that the classical ring of
Witt vectors, with all its concomitant structure, can be understood in a
formula-free way in terms of a plethystic version of an affine blow-up applied
to the plethory generated by the Frobenius map. We also discuss the linear and
infinitesimal structure of plethories and explain how this gives...
147.
Algebra for Distributed Data Sources
- Iztok Savnik
The algebra for distributed data sources includes standard operations on sets which evolved from the relational and nested-relational algebras, the operations for querying the conceptual schemata, and the operations which allow for the manipulation of distributed objects. The algebra serves as the basis for the prototype implementation of the query optimizer for distributed data sources. The design of the query optimizer is rooted in the architecture of the relational and object-relational query optimizers. Keywords: database algebras, query languages, query optimization, distributed databases, and Web query languages. 1 Introduction The Internet contains large amount of different data sources accessible through ftp...
148.
Towards Deformed Chiral Algebras
- Frenkel, Edward; Reshetikhin, Nikolai
We describe a new algebraic structure of "deformed chiral algebra" motivated
by the study of the deformed W-algebras. We use it to gain some insights into
the deformed Virasoro algebra.
149.
$A^{N}_{\infty}$-algebras
- Angel, Mauricio; Diaz, Rafael
We study higher depth algebras. We introduce several examples of such
structures starting from the notion of $N$-differential graded algebras and
build up to the concept of $A_{\infty}^N$-algebras.
150.
An Elementary Construction of the Geometric Algebra
- Alan Macdonald
We give a simple, elementary, direct, and motivated construction of the geometric algebra over R^n.
151.
Cyclotomic Schur algebras and blocks of cyclic defect
- Steffen König; Cyclotomic Schur Algebras
An explicit classification is given of blocks of cyclic defect of cyclotomic Schur algebras and of cyclotomic Hecke algebras, over discrete valuation rings. 1991 Mathematics Subject Classification: Primary 20G05, 20C20. Secondary 16G30, 17B37, 57M25. 1 Introduction A fundamental result of representation theory of finite groups is the classification of blocks of cyclic defect. The aim of this note is to use this classification as a tool for classifying blocks of cyclotomic Hecke algebras and of the associated Schur algebras, over discrete valuation rings. This reproves and generalizes results of Xi and of Erdmann for classical Schur algebras over fields. We...
152.
Cyclotomic Schur algebras and blocks of cyclic defect
- Steffen Konig; Cyclotomic Schur Algebras
An explicit classification is given of blocks of cyclic defect of cyclotomic Schur algebras and of cyclotomic Hecke algebras, over discrete valuation rings. 1991 Mathematics Subject Classification: Primary 20G05, 20C20. Secondary 16G30, 17B37, 57M25. 1 Introduction A fundamental result of representation theory of finite groups is the classification of blocks of cyclic defect. The aim of this note is to use this classification as a tool for classifying blocks of cyclotomic Hecke algebras and of the associated Schur algebras, over discrete valuation rings. This reproves and generalizes results of Xi and of Erdmann for classical Schur algebras over fields. We...
153.
On contractibility of matrix algebras
- Moslehian, Mohammed Sal; Department of Maths., Ferdowsi University, Mashhad 91775, Iran
; msalm@math.um.ac.ir; Niknam, Assadollah; Department of Maths., Ferdowsi University, Mashhad 91775, Iran
; niknam@math.um.ac.ir
We show first that for each C*algebra
A, contractibility of
A implies
contractibility of
Mn(
A).
We next prove that an incidence algebra
A of upper
triangular matrices, defined by a partially ordered set Ω on {1, 2,...,
n}
satisfying (
p, q) ∈ Ω ⇒
p ≤
q, is a contractible
Banach
algebra if there is no discordant coupled of D-transitive triples of elements
of Ω.
Mathematics Subject
Classification (2000):
Primary 46H05, 46H25; Secondary 15A99
Quaestiones Mathematicae 25 (2002), 327-332
154.
A Short Proof of Representability of Fork Algebras
- Viktor Gyuris
In this paper a strong relation is demonstrated between fork algebras and quasi-projective relation algebras. With the help of the representation theorem of quasi-projective relation algebras, a short proof is given for the representation theorem of fork algebras. Keywords: fork algebras, quasi-projective relation algebras, relation algebras, representation theorem, algebraic logic, theoretical computer science, program specification Fork algebras, due to their expressive power and applicability in computing science, have been intensively studied in the last four years. Their literature is alive and productive. See e.g. Veloso--Haeberer [21], [22], [2], [6], [5], [7], Sain--Simon [17]. As described in the textbook [12, 2.7.46],...
155.
Deformations of Azumaya algebras
- Bressler, P.; Gorokhovsky, A.; Nest, R.; Tsygan, B.
In this paper we compute the deformation theory of a special class of
algebras, namely of Azumaya algebras on a manifold ($C^{\infty}$ or complex
analytic).
156.
Cuntz-like algebras
- Renault, Jean
The usual crossed product construction which associates to the homeomorphism
$T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended
to the case of a partial local homeomorphism $T$. For example, the
Cuntz-Krieger algebras are the C$^*$-algebras of the one-sided Markov shifts.
The generalizations of the Cuntz-Krieger algebras (graph algebras, algebras
$O_A$ where $A$ is an infinite matrix) which have been introduced recently can
also be described as C$^*$-algebras of Markov chains with countably many
states. This is useful to obtain such properties of these algebras as
nuclearity, simplicity or pure infiniteness. One also gives examples of strong
Morita equivalences arising from dynamical systems equivalences.
157.
Viewing AF-algebras as graph algebras
- Drinen, D.
Every AF-algebra arises as a graph algebra in the sense of Kumjian, Pask,
Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by
Stratila and Voiculescu is consistent with Kumjian's notion of diagonal, and
the groupoid arising from a well-chosen Bratteli diagram for A coincides with
Kumjian's twist groupoid constructed from a diagonal of A.
158.
When a C*-algebra is a coefficient algebra for a given endomorphism
- Bakhtin, V. I.; Lebedev, A. V.
The paper presents a criterion for a C*-algebra to be a coefficient algebra
associated with a given endomorphism
159.
Deformation of algebras over the Landweber-Novikov algebra
- Yau, Donald
An algebraic deformation theory of algebras over the Landweber-Novikov
algebra is obtained.
160.
q-deformed W-algebras and elliptic algebras
- Avan, J.; Frappat, L.; Rossi, M.; Sorba, P.
The elliptic algebra A_{q,p}(sl(N)_{c}) at the critical level c=-N has an
extended center containing trace-like operators t(z). Families of Poisson
structures, defining q-deformations of the W_N algebra, are constructed. The
operators t(z) also close an exchange algebra when (-p^{1/2})^{NM} = q^{-c-N}
for M \in Z. It becomes Abelian when in addition p=q^{Nh} where h is a non-zero
integer. The Poisson structures obtained in these classical limits contain
different q-deformed W_N algebras depending on the parity of h, characterizing
the exchange structures at p =/ q^{Nh} as new W_{q,p}(sl(N)) algebras.
