Counting Finite-Dimensional Algebras Over Finite Field

enumerating algebras over a finite field

‎we obtain the porc formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field gf$(q)$‎. ‎we also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over gf$(q)$‎.

enumerating algebras over a finite field

‎we obtain the porc formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field gf$(q)$‎. ‎we also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over gf$(q)$.

Finite Dimensional Pointed Hopf Algebras over S

Finite Dimensional Hecke Algebras

This article surveys development on finite dimensional Hecke algebras in the last decade. In the first part, we explain results on canonical basic sets by Geck and Jacon and propose a categorification framework which is suitable for our example of Hecke algebras. In the second part, we review basics of Kashiwara crystal and explain the Fock space theory of cyclotomic Hecke algebras and its appl...

On permutably complemented subalgebras of finite dimensional Lie algebras

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...