An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension

By T. Lenagan, Agata Smoktunowicz. 2005

49 citations recorded by the source corpus.

The famous 1960's construction of Golod and Shafarevich yields infinite dimensional nil, but not nilpotent, algebras. However, these algebras have exponential growth. Here, we construct an infinite dimensional nil, but not locally nilpotent, algebra which has polynomially bounded growth.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/68aa76d1306dc37d7c5a2ca8b033ec4921aef9ba

Citations in the corpus

• Combinatorial algebra : syntax and semantics (2014, unknown): “Golod’s construction was essentially the only known construction of counterexamples to Kurosh’s problem untill 2007 when a new (syntactic!) method was developed by Lenagan and Smoktunowicz in [200].”