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Toupie algebra, some examples of laura algebras
Toupie algebra laura algebras
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2010/11/24
We consider the bound quiver algebras whose ordinary quiver is that of a canonical algebra. We determine which of those algebras are hereditary, tilted, quasitilted, weakly shod or laura algebras.
Bijective evaluation of the connection coefficients of the double coset algebra
Bijective evaluation the connection coefficients
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2010/11/24
This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this s...
Category O for the rational Cherednik algebra associated to the complex reflection group G_12
the rational Cherednik algebra the complex reflection group G_12
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2010/11/23
In this paper, we describe the irreducible representations in category O of the rational Cherednik algebra H_c(G_12,h) associated to the complex reflection group G_12 with reflection representation h ...
Cyclotomic Temperley-Lieb algebra of type D and its representation theory
Cyclotomic Temperley-Lieb algebra representation theory
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2010/11/23
We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Te...
The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach
The Clifford Algebra Quantum Mechanics
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2010/11/23
In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to constr...
The Clifford Algebra approach to Quantum Mechanics A: The Schroedinger and Pauli Particles
The Clifford Algebra approach Quantum Mechanics
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2010/11/23
In this paper we show how all the quantum properties of Schroedinger and Pauli particles can be described entirely from within a Clifford algebra taken over the reals. There is no need to appeal to a...
On the stability of weight spaces of enveloping algebra in prime characteristic
enveloping algebra prime characteristic
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2010/11/15
By the result of Dixmier, any weight space of enveloping algebra of Lie algebra L over a field of characteristic 0 is adL stable. In this paper we will show that this result need not be true, if F is...
A non-weakly amenable Banach algebra whose bidual is weakly amenable
Banach algebra weakly amenable
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2010/11/9
We answer, in the negative, the question: Does a Banach algebra inherit weak amenability from its bidual?, which was open since 1996
On twin and anti-twin words in the support of the free Lie algebra
On twin anti-twin words the free Lie algebra
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2010/11/11
Let $L_{K}(A)$ be the free Lie algebra on a finite alphabet $A$ over a commutative ring $K$ with unity. For a word $u$ in the free monoid $A^{*}$ let $\tilde{u}$ denote its reversal. Two words in $A^...
Degree growth of monomial maps and McMullen's polytope algebra
monomial maps McMullen's polytope algebra
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2010/11/18
We compute all dynamical degrees of monomial maps. Our approach is based on the isomorphism between the polytope algebra of P. McMullen and the universal cohomology of complete toric varieties.
Irreducible Highest Weight Representations Of The Simple n-Lie Algebra
Irreducible Highest Weight Representations The Simple n-Lie Algebra
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2010/11/11
A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of ...
On the algebraic set of singular elements in a complex simple Lie algebra
algebraic singular elements
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2010/11/19
Let $G$ be a complex simple Lie group and let $\g = \hbox{\rm Lie}\,G$. Let $S(\g)$ be the $G$-module of polynomial functions on $\g$ and let $\hbox{\rm Sing}\,\g$ be the closed algebraic cone of sin...
The Hopf algebra of diagonal rectangulations
The Hopf algebra diagonal rectangulations
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2010/11/15
We define and study a combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square. This Hopf algebra provides an intrinsic combinatorial realization of the Hop...
A Generalization of the Weak Amenability of some Banach Algebra
Generalization Banach Algebra
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2010/11/9
Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under g...
The Freudenthal product and orbits in the Jordan algebra over the exceptional Lie group of type F$_{4(-20)}$
Freudenthal orbits Jordan algebra
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2010/11/9
The orbit decomposition is presented for the real form of complex simple Jordan algebra with the automorphism group F$_{4(-20)}$, explicitly, in terms of the cross product and the characteristic polyn...