Combinatorics of transformations from standard to non-standard bases in Brauer algebras

Standard Lyndon bases of Lie algebras and enveloping algebras

It is well known that the standard bracketings of Lyndon words in an alphabet A form a basis for the free Lie algebra Lie(A) generated by A . Suppose that g 2 Lie(A)/J is a Lie algebra given by a generating set A and a Lie ideal J of relations. Using a Grobner basis type approach we define a set of "standard" Lyndon words, a subset of the set Lyndon words, such that the standard bracketings of ...

Based Algebras and Standard Bases for Quasi-hereditary Algebras

Quasi-hereditary algebras can be viewed as a Lie theory approach to the theory of finite dimensional algebras. Motivated by the existence of certain nice bases for representations of semisimple Lie algebras and algebraic groups, we will construct in this paper nice bases for (split) quasi-hereditary algebras and characterize them using these bases. We first introduce the notion of a standardly ...

On non-standard graded algebras

Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.

Algebras from Standard Constructions

Standard and Non-standard Extensions of Lie algebras

We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root α+4, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no loops between the dots, while it is possible if α+4 is a Borcherds imaginary simple root. We also comment on the root lattices of these new algebras. The folding proced...