2017/06/21 by K. R. Goodearl, Goodearl, K. R., Milen Yakimov +1
Mathematics · Physics and Astronomy · #13F60 #16K40 #16S85 #16T20 #16W50 #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1706.06957
openalex publication_date 2017/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define two invariants for (semiprime right Goldie) algebras, one for algebras graded by arbitrary abelian groups, which is unchanged under twists by 2-cocycles on the grading group, and one for \mathbb Z-graded or \mathbb Z≥ 0-filtered algebras. The first invariant distinguishes quantum algebras which are "truly multiparameter" apart from ones that are "essentially uniparameter", meaning cocycle twists of uniparameter algebras. We prove that both invariants are stable under adjunction of polynomial variables. Methods for computing these invariants for large families of algebras are given, including quantum nilpotent algebras and algebras admitting one quantum cluster, and applications to non-isomorphism theorems are obtained.