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Dive into the research topics where Sergei O. Ivanov is active.

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Featured researches published by Sergei O. Ivanov.


Journal of Pure and Applied Algebra | 2015

A higher limit approach to homology theories

Sergei O. Ivanov; Roman Mikhailov

A lot of well-known functors such as group homology, cyclic homology of algebras can be described as limits of certain simply defined functors over categories of presentations. In this paper, we develop a technique for the description of the higher limits over categories of presentations and show that certain homological functors can be described in this way. In particular, we give a description of Hochschild homology and the derived functors of tensor, symmetric and exterior powers in the sense of Dold and Puppe as higher limits.


Journal of Algebra | 2014

Stable Calabi–Yau dimension of self-injective algebras of finite type

Sergei O. Ivanov; Yury Volkov

Abstract We give an equivalent definition of the stable Calabi–Yau dimension in terms of bimodule syzygies and so-called stably inner automorphisms. Using it, we complete the computation of the stable Calabi–Yau dimensions of the self-injective algebras of finite representation type which was started by K. Erdmann, A. Skowronski, J. Bialkowski and A. Dugas.


Israel Journal of Mathematics | 2018

On lengths of Hℤ-localization towers

Sergei O. Ivanov; Roman Mikhailov

In this paper, the Hℤ-length of different groups is studied. By definition, this is the length of the Hℤ-localization tower or the length of the transfinite lower central series of Hℤ-localization. It is proved that, for a free noncyclic group, its Hℤ-length is ≥ ω+2. For a large class of ℤ[C]-modules M, where C is an infinite cyclic group, it is proved that the Hℤ-length of the semi-direct product M ⋊ C is ≤ ω + 1 and its Hℤ-localization can be described as a central extension of its pro-nilpotent completion. In particular, this class covers modules M, such that M⋊C is finitely presented and H2(M ⋊ C) is finite.


Journal of Mathematical Sciences | 2010

On the construction of bimodule resolutions with the help of the Happel lemma

Yu. V. Volkov; A. I. Generalov; Sergei O. Ivanov


Journal of Mathematical Sciences | 2012

Nakayama functors and Eilenberg-Watts theorems

Sergei O. Ivanov


Advances in Mathematics | 2016

On a problem of Bousfield for metabelian groups

Sergei O. Ivanov; Roman Mikhailov


Journal of Algebra | 2015

BV structure on Hochschild cohomology of the group ring of quaternion group of order eight in characteristic two

Alexander Ivanov; Sergei O. Ivanov; Yury Volkov; Guodong Zhou


Journal of Mathematical Sciences | 2013

Self-Injective algebras of stable Calabi-Yau dimension three

Sergei O. Ivanov


arXiv: Group Theory | 2015

Higher limits, homology theories and fr-codes

Sergei O. Ivanov; Roman Mikhailov


Journal of Mathematical Sciences | 2009

Bimodule resolution of a group algebra

A. I. Generalov; Sergei O. Ivanov

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Roman Mikhailov

Saint Petersburg State University

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Jie Wu

National University of Singapore

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A. I. Generalov

Saint Petersburg State University

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Yury Volkov

Saint Petersburg State University

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Alexander Ivanov

Saint Petersburg State University

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Guodong Zhou

East China Normal University

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A. A. Ivanov

Saint Petersburg State University

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Alexander A. Ivanov

Saint Petersburg State University

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Vladimir A. Sosnilo

Saint Petersburg State University

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Yu. V. Volkov

Saint Petersburg State University

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