2021/11/18 by А. С. Гордиенко, Alexey Gordienko, Gordienko, Alexey
Mathematics · #14L17 #16R10 #16R50 #16T05 #16T10 #16T15 #16Wxx (Primary) #17A01 #17A36 #17Bxx #18Axx #18D20 #20C30 #20E26 #20F05 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AG #math.CT #math.KT #math.QA #math.RA #msc:14L17 #msc:16R10 #msc:16R50 #msc:16T05 #msc:16T10 #msc:16T15 #msc:16Wxx #msc:17A01 #msc:17A36 #msc:17Bxx #msc:18Axx #msc:18D20 #msc:20C30 #msc:20E26 #msc:20F05
paper · pdf · doi:10.48550/arxiv.2111.09810
386 pages, in Russian; minor misprints corrected; based on arXiv:1112.6245, arXiv:1203.5384, arXiv:1205.0778, arXiv:1207.1699, arXiv:1210.2528, arXiv:1211.1272, arXiv:1212.1321, arXiv:1301.2446, arXiv:1309.3664, arXiv:1402.5272, arXiv:1409.0151, arXiv:1505.02893, arXiv:1508.03764, arXiv:1511.01860, arXiv:1704.07170, arXiv:1705.05809, arXiv:1805.04073, arXiv:1812.04563, arXiv:2005.12954
openalex publication_date 2021/11/18 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28 · arxiv created 2026/08/01 · arxiv updated 2026/08/04
This manuscript is an extended version of the author's habilitation thesis defended on May 21, 2021 at M.V. Lomonosov Moscow State University. It is devoted to the study of (co)stability of radicals, existence of (co)invariant Levi and Wedderburn decompositions, structure of the corresponding simple algebras and codimension growth of polynomial identities in (co)module algebras over bi- and Hopf algebras and their generalizations. The main difference between this manuscript and the "official" thesis are additional chapters dealing with equivalences of gradings and Hopf algebra (co)actions, V-universal (co)acting bi- and Hopf algebras and related categorical questions. (In Russian.)