2016/01/27 by Yuqun Chen, Chen, Yuqun, Jianjun Qiu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1603.01454
Let \mathfraka,\mathfrakb,\mathfrake be algebras over a field k. Then \mathfrake is an extension of \mathfraka by \mathfrakb if \mathfraka is an ideal of \mathfrake and \mathfrakb is isomorphic to the quotient algebra \mathfrake/\mathfraka. In this paper, by using Gröbner-Shirshov bases theory for associative (resp. Lie) algebras, we give complete characterizations of associative (resp. Lie) algebra extensions of \mathfraka by \mathfrakb, where \mathfrakb is presented by generators and relations.