Year: 2026
Type: article
Abstract: Let G be a finite abelian group and let K be an algebraically closed field of characteristic 0. We consider associative unital algebras A over K graded by G , that is $$A=\oplus _{g\in G} A_g$$ A = ⊕ g ∈ G A g , where the vector subspaces $$A_g$$ A g satisfy $$A_gA_h\subseteq A_{g+h}$$ A g A h ⊆ A g + h for every g , $$h\in G$$ h ∈ G . Such a G -grading is called regular whenever for every n -tuple $$(g_1,\ldots ,g_n)\in G^n$$ ( g 1 , … , g n ) ∈ G n there exist homogeneous elements $$a_i\in A_{g_i}$$ a i ∈ A g i such that $$a_1\cdots a_n\ne 0$$ a 1 ⋯ a n ≠ 0 in A ; furthermore, for every g , $$h\in G$$ h ∈ G and every $$a_g\in A_g$$ a g ∈ A g , $$a_h\in A_h$$ a h ∈ A h
Authors: Lucio Centrone, Plamen Koshlukov, Kauê Pereira
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
OpenAlex ID: W7171035775