1996/11/14 by Vyacheslav Artamonov, Vyacheslav A. Artamonov, Artamonov, Vyacheslav +3
Mathematics · #Action (physics) #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Commutative property #Division algebra #FOS: Mathematics #Finite Group Theory Research #Generalization #Hopf algebra #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum Algebra (math.QA) #Quasitriangular Hopf algebra #Representation theory of Hopf algebras #Subalgebra #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9611017
10 pages, LaTeX, this parer is revised and completed compilation of two separate papers, both to appear in "Vestnik Moskovskogo Universiteta" ("The Herald of Moscow State University") in 1996-1997
arxiv created 1996/11/14 · openalex publication_date 1996/11/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Action of finite-dimensional Hopf algebra H on commutative k-algebra A is considered. As a generalization of the well-known fact for finite groups S. Montgomery raised a problem in 1993 whether A is integral over subalgebra of invariants AH. Recently some new results were obtained. Using the properties of coradical filtration of pointed Hopf algebras we verified the truth of the hypothesis in tree different cases: 1) Hopf algebra H is commutative; 2) char k = p > 0; 3) A is integral domain. In spite of numerous partial positive results it turned out that hypothesis of S. Montgomery isn't true in general. The counteraxamples were built for series of pointed Hopf algebras AN, N ≥ 2.