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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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1572-9176
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Volume 26, Issue 2

Dihedral ∞-simplicial modules and dihedral homology of involutive homotopy unital A∞-algebras

Sergey V. Lapin
Published Online: 2019-04-06 | DOI: https://doi.org/10.1515/gmj-2019-2018

Abstract

The notion of a dihedral $\mathrm{\infty }$-simplicial module is introduced. The homotopy invariance of the structure of a dihedral $\mathrm{\infty }$-simplicial module is proved. The concept of the dihedral homology of a dihedral $\mathrm{\infty }$-simplicial module is developed. The notion of an involutive homotopy unital ${A}_{\mathrm{\infty }}$-algebra is introduced. The dihedral $\mathrm{\infty }$-simplicial module is constructed using an involutive homotopy unital ${A}_{\mathrm{\infty }}$-algebra. The concept of the dihedral homology of an involutive homotopy unital ${A}_{\mathrm{\infty }}$-algebra is developed. For the dihedral homology of involutive homotopy unital ${A}_{\mathrm{\infty }}$-algebras, the analogue of the Krasauskas–Lapin–Solov’ev exact sequence is obtained.

MSC 2010: 55U10; 18G30; 55U43

Dedicated to Professor N. Berikashvili on the occasion of his 90th birthday

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Accepted: 2019-02-05

Published Online: 2019-04-06

Published in Print: 2019-06-01

Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 257–286, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X,

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