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Asymptotic Hecke algebras and involutions
Asymptotic Hecke algebras involutions Representation Theory
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2012/4/17
In a previous paper the author and D. Vogan defined and studied a Hecke algebra module structure on a vector space spanned by the involutions in a Weyl group. In this paper this study is continued by ...
Graded Skew Clifford Algebras that are Twists of Graded Clifford Algebras
regular algebra Clifford algebra skew Clifford algebra twist by an automorphism
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2012/4/17
We prove that if $A$ is a regular graded skew Clifford algebra and is a twist of a regular graded Clifford algebra $B$ by an automorphism, then the subalgebra of $A$ generated by a certain normalizing...
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...
Covariant Mickelsson-Faddeev extensions of gauge and diffeomorphism algebras
Covariant Mickelsson-Faddeev extensions of gauge diffeomorphism algebras Mathematical Physics
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2012/5/31
We construct new extensions of current and diffeomorphism algebras in N>3 dimensions, which are related to the Mickelsson-Faddeev algebra. The result is compatible with Dzhumadil'daev's classification...
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 ...