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Skein algebras and cluster algebras of marked surfaces
Skein algebras cluster algebras marked surfaces Quantum Algebra Geometric Topology
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2012/4/17
This paper defines several algebras associated to an oriented surface S with a finite set of marked points on the boundary. The first is the skein algebra Sk_q(S), which is spanned by links in the sur...
Representations of solvable Lie algebras with filtrations
Representations solvable Lie algebras filtrations
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2012/3/1
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are fou...
The Brauer-Picard group of the representation category of finite supergroup algebras
Brauer-Picard group tensor category module category Quantum Algebra
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2012/2/29
We develop further the techniques presented in [M. Mombelli. On the tensor product of bimodule categories over Hopf algebras. Preprint arXiv:1111.1610 ] to study bimodule categories over the represent...
Classification of finite dimensional irreducible modules over W-algebras
Classification of finite dimensional irreducible modules over W-algebras
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2012/2/29
Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of charact...
Cartan MASAs in von Neumann Algebras are Norming and a New Proof of Mercer's Theorem
Norming algebra Cartan MASA C*-diagonal
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2012/3/1
In this note we observe that a result of Sinclair and Smith together with the Feldman-Moore description of a von Neumann algebra with a Cartan MASA shows that Cartan MASAs are norming. We also use the...
Monomial bases of quantized enveloping algebras of finite type
quantized enveloping algebra Hall algeba monomial basis
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2011/9/28
In this paper we present a systematic construction of monomial bases for all quantized enveloping algebras of finite type, which generalizes the main result in [4] for simply laced case.
On Pseudo-BCI Algebras with Condition (pP)
pseudo-BCK algebra pseudo-BCI algebra pseudo-BCI algebra with condition (pP)
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2011/9/25
As a generalization of BCI-algebras with condition (S) and pseudo-BCK algebras with condition (pP), the notion of pseudo-BCI algebras with condition (pP) is introduced. An example of pseudo-BCI algebr...
On $0$-Schur algebras
$0$-Schur algebra representation type presentation
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2011/9/24
Based on a geometricconstruction of quantum Schur algebras due to Beilinson, Lusztig andMacPherson and the structure of $0$-Hecke algebras, we give apresentation for $0$-Schur algebras and determine t...
Polynomials of almost-normal arguments in $C^*$-algebras
Polynomials of almost-normal arguments Operator Algebras
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2011/9/23
Abstract: The functional calculus for normal elements in $C^*$-algebras is an important tool of Analysis. We suggest an approximate substitute for such calculus for elements $a$ with the small self-co...
SK_1 and Lie Algebras
uniform group Iwasawa algebra SK1 Lie algebra
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2011/9/23
Abstract: We investigate the vanishing of the group SK1(A(G)) for the Iwasawa algebra A(G) of a pro-p p-adic Lie group G (with p different from 2). We reduce this vanishing to a linear algebra problem...
Category O for Rational Cherednik Algebras H_{t,c}(GL_2(F_p),h) in Characteristic p
Rational Cherednik Algebras Characteristic p Representation Theory
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2011/9/23
Abstract: In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive charac...
Symmetric hyperbolic systems in algebras of generalized functions and distributional limits
Symmetric hyperbolic systems distributional limits Analysis of PDEs
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2011/9/23
Abstract: We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential ...
Tying up baric algebras
Baric algebra Indecomposable baric algebra Rings and Algebras
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2011/9/23
Abstract: Given two baric algebras $(A_1,\omega_1)$ and $(A_2,\omega_2)$ we describe a way to define a new baric algebra structure over the vector space $A_1\oplus A_2$, which we shall denote $(A_1\bo...
On embedding of dendriform algebras into Rota---Baxter algebras
dendriform algebras Rota Baxter algebras
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2011/9/29
Abstract: Following a recent work by C. Bai, O. Bellier, L. Guo, and X. Ni (arXiv:1106.6080) we define what is a dendriform di- or trialgebra in an arbitrary variety Var of algebras (associative, comm...
Solvability of the $H^\infty$ algebraic Riccati equation in Banach algebras
Riccati equations Banach algebras Systems over rings H1 control Spatially distributed dynamical systems
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2011/9/21
Abstract: Let $R$ be a commutative complex unital semisimple Banach algebra with the involution $\cdot ^\star$. Sufficient conditions are given for the existence of a stabilizing solution to the $H^\i...