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MOD-2 (CO)homology of an Abelian Group. / Ivanov, S. O.; Zaikovskii, A. A.
в: Journal of Mathematical Sciences (United States), Том 252, 2021, стр. 794–803.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - MOD-2 (CO)homology of an Abelian Group
AU - Ivanov, S. O.
AU - Zaikovskii, A. A.
N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021
Y1 - 2021
N2 - It is known that for a prime p ≠ = 2, there is the following natural description of the homology algebra of an Abelian group H*(A, p) ≅ Λ(A/p)⊗Γ(pA), and for finitely generated Abelian groups there is the following description of the cohomology algebra of H*(A, p) ≅ Λ((A/p)∨)⊗Sym((pA)∨). It is proved that for p = 2, there are no such descriptions “depending” on A/2 and 2A only. Moreover, natural descriptions of H*(A, 2) and H*(A, 2), “depending” on A/2, 2A, and a linear map β¯ : 2A → A/2 are presented. It is also proved that there is a filtration by subfunctors on Hn(A, 2), whose quotients are Λn−2i(A/2)⊗Γi(2A), and there is a natural filtration on Hn(A, 2) for finitely generated Abelian groups, whose quotients are Λn−2i((A/2)∨) ⊗ Symi((2A)∨).
AB - It is known that for a prime p ≠ = 2, there is the following natural description of the homology algebra of an Abelian group H*(A, p) ≅ Λ(A/p)⊗Γ(pA), and for finitely generated Abelian groups there is the following description of the cohomology algebra of H*(A, p) ≅ Λ((A/p)∨)⊗Sym((pA)∨). It is proved that for p = 2, there are no such descriptions “depending” on A/2 and 2A only. Moreover, natural descriptions of H*(A, 2) and H*(A, 2), “depending” on A/2, 2A, and a linear map β¯ : 2A → A/2 are presented. It is also proved that there is a filtration by subfunctors on Hn(A, 2), whose quotients are Λn−2i(A/2)⊗Γi(2A), and there is a natural filtration on Hn(A, 2) for finitely generated Abelian groups, whose quotients are Λn−2i((A/2)∨) ⊗ Symi((2A)∨).
UR - http://www.scopus.com/inward/record.url?scp=85099462694&partnerID=8YFLogxK
U2 - 10.1007/s10958-021-05200-0
DO - 10.1007/s10958-021-05200-0
M3 - Article
AN - SCOPUS:85099462694
VL - 252
SP - 794
EP - 803
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
ER -
ID: 90651145