相关论文: On some properties of LS algebras

Cassidy, Phan and Shelton associate to any regular cell complex X a quadratic K-algebra R(X). They give a combinatorial solution to the question of when this algebra is Koszul. The algebra R(X) is a combinatorial invariant but not a…

The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When…

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective. For a separable Frobenius extension between Artin algebras,…

It is shown that any compact semistable quotient (in the sense of Heinzner and Snow) of a normal algebraic variety by a complex reductive Lie group $G$ is a good quotient. This reduces the investigation and classification of such…

An infinite filiform Lie algebra L is residually nilpotent and its graded associated with respect to the lower central series has smallest possible dimension in each degree but is still infinite. This means that gr(L) is of dimension two in…

The exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $SL_2^n$-structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so…

We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the…

The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable…

The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA/0612798. We prove that generically their action on…

We call a finite-dimensional K-algebra A geometrically irreducible if for all d, all connected components of the affine scheme of d-dimensional A-modules are irreducible. We show that the geometrically irreducible algebras without loops…

Toroidal Lie algebras are $n$ variable generalizations of affine Kac-Moody Lie algebras. Full toroidal Lie algebra is the semidirect product of derived Lie algebra of toroidal Lie algebra and Witt algebra, also it can be thought of…

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank…

We construct and study a family of toric degenerations of the algebra of conformal blocks for a stable marked curve $(C, \vec{p})$ with structure group $SL_3(\mathbb{C}).$ We find that this algebra is Gorenstein. For the genus $0, 1$ cases…

In an attempt to get some information on the multiplicative structure of the Green ring we study algebraic modules for simple groups, and associated groups such as quasisimple and almost-simple groups. We prove that, for almost all groups…

In this note we first study regular $\mathbb{Z}$-graded local rings. We characterize commutative noetherian regular $\mathbb{Z}$-graded local rings in similar ways as in the usual local case. Then, we characterize graded isolated…

In this paper we prove that every coefficient of twisted Alexander polynomials of torus knots associated with irreducible $\mathrm{SL}_n(\Bbb C)$-representations is an $\Bbb A$-valued locally constant function on the $\mathrm{SL}_n(\Bbb…

For every absolutely irreducible orthogonal representation of a twisted form of SL2 over a field of characteristic zero, we compute the "unique" symmetric bilinear form that is invariant under the group action. We also prove the analogous…

A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation…

We compare by a very elementary approach the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones. Examples are given of coupled cocycles. Some properties are deduced as to Leibniz deformations. We also…