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On Lie algebroids and Poisson algebras     Lie algebroids  Poisson algebras  faithful modules  Differential Geometry       font style='font-size:12px;'> 2011/7/27
Abstract: We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classificati...
Abstract: A procedure to construct $K$-matrices from the generalized $q$-Onsager algebra $\cO_{q}(\hat{g})$ is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-numb...
On representations of cyclotomic Hecke algebras      representations  cyclotomic Hecke algebras        font style='font-size:12px;'> 2011/2/28
An approach, based on Jucys–Murphy elements, to the representation theory of cy-clotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra)of the set of the Jucys–Murphy ele...
An open question, raised independently by several authors, asks if a closed amenable subalgebra of B(H) must be similar to an amenable C-algebra; the question remains open even for singly-generated ...
Presentations and Tietze Transformations of C*-algebras      C*-algebra  Unitization  Adjoint Functor  Free Construction       font style='font-size:12px;'> 2011/1/18
In this work, I develop a new view of presentation theory for C*-algebras, both unital and non-unital, heavily grounded in classical notions from algebra. In particular, I introduce Tietze transformat...
The Gel’fand-Shilov spaces of type S are considered as topological algebras with respect to the Moyal star product and their corresponding algebras of multipliers are defined and investigated.
Let p be a prime integer, 1 ≤ s ≤ r integers, F a field of characteristic p.
Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are Lie algebras of volume-preserving transformation groups. They are simple in generic case. Dokovic and Zhao fo...
On the Returning Arrows of Graded Self-injective Algebras      Arrows  Graded Self-injective Algebras        font style='font-size:12px;'> 2011/2/24
A translation quiver Q is a quiver with a mono quiver map ,called translation, defined on a subset of the vertices. Recently, varies construction gives rise to quiver obtained from the original one b...
Weyl modules for multiloop algebras     Weyl modules  multiloop algebras       font style='font-size:12px;'> 2011/2/25
Global and local Weyl modules for the untwisted multiloop Lie algebras were defined in [CFK] via homological properties. In this paper we extended the ideas to give a categorical definition of the Wey...
It is a folklore fact that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion m...
On Engel's Theorem for Leibniz algebras      Leibniz algebras  nilpotent  Engel’s Theorem.       font style='font-size:12px;'> 2011/1/17
I give a simpler proof of the generalisation of Engel’s Theorem to Leibniz algebras.
Isotopes of Hurwitz algebras      Isotopes  Hurwitz algebras        font style='font-size:12px;'> 2011/1/19
We study algebras that are isotopic to Hurwitz algebras. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. An explicit, geometrically intutive descript...
Bases for partially commutative Lie algebras      Bases  partially commutative Lie algebras        font style='font-size:12px;'> 2011/1/18
In this paper, linear bases for the partially commutative Lie alge-bras are found. The method of the Gr¨obner–Shirshov bases is used.
The u-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types gl(n), sp(2n) and so(2n) are obtained.As a consequence, we recover the Enright...

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