Factorization of Graded Traces on Nichols Algebras

On a Factorization of Graded Hopf Algebras Using Lyndon Words

We find a generalization of the restricted PBW basis for pointed Hopf algebras over abelian groups constructed by Kharchenko. We obtain a factorization of the Hilbert series for a wide class of graded Hopf algebras. These factors are parametrized by Lyndon words, and they are the Hilbert series of certain graded Hopf algebras.

On Associativity of Graded Algebras

Necessary and sufficient conditions are given to guarantee associativity of algebras and co-algebras. As main application, it is discussed the associativity of the tensor algebra T (V ) of a free module V over any commutative ring R. 1. Review of basic definitions Recall that a vector space A, or more generally a (free) module over a commutative ring R is an R-algebra if a multiplication map mA...

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Involutions on graded matrix algebras

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.