A Normal form for HNN-extension of Dialgebras

Groebner-Shirshov bases for dialgebras

In this paper, we define the Gröbner-Shirshov basis for a dialgebra. The Composition-Diamond lemma for dialgebras is given then. As results, we give Gröbner-Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.

A new Composition-Diamond lemma for dialgebras

Let $Di\langle X\rangle$ be the free dialgebra over a field generated by a set $X$. Let $S$ be a monic subset of $Di\langle X\rangle$. A Composition-Diamond lemma for dialgebras is firstly established by Bokut, Chen and Liu in 2010 \cite{Di} which claims that if (i) $S$ is a Gröbner-Shirshov basis in $Di\langle X\rangle$, then (ii) the set of $S$-irreducible words is a linear basis of the quotient dialgebra $Di\langle X \mid S \rangle$, but not conversely. Such a lemma based on a fixed ordering on normal diwords of $Di\langle X\rangle$ and special definition of composition trivial modulo $S$. …

李超代数的HNN扩张

HNN extensions of Lie superalgebras

本文明确刻画了李超代数HNN扩张的结构，证明其为原代数与自由李超代数的直和，并用于研究有限表示李超代数中理想的有限生成性，同时发展了Gröbner-Shirshov基理论。

Nijenhuis李代数的嵌入定理

An embedding theorem for Nijenhuis Lie algebras

本文研究了Nijenhuis李代数的HNN扩展，并证明了其嵌入定理，利用Gröbner-Shirshov基理论寻找正常形式。