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Zap. Nauchn. Sem. POMI, 2011, Volume 394, Pages 226–261 (Mi znsl4636)  

This article is cited in 1 scientific paper (total in 1 paper)

Selfinjective algebras of stable Calabi–Yau dimension three

S. O. Ivanov

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: In the present paper, we introduce the class of algebras, which allows the so-called DTI-family of relations. With few exceptions, the stable Calabi–Yau dimension of these algebras is equal to 3. We prove that all algebras of quaternion type are contained in this class, and we give some other examples of such algebras. Furthermore, we describe minimal projective bimodule resolutions for algebras from this class.

Key words and phrases: Calabi–Yau dimension, stable module category, selfinjective algebra, path algebra of a quiver with relations.

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English version:
Journal of Mathematical Sciences (New York), 2013, 188:5, 601–620

Bibliographic databases:

Document Type: Article
UDC: 512
Received: 08.09.2011

Citation: S. O. Ivanov, “Selfinjective algebras of stable Calabi–Yau dimension three”, Problems in the theory of representations of algebras and groups. Part 22, Zap. Nauchn. Sem. POMI, 394, POMI, St. Petersburg, 2011, 226–261; J. Math. Sci. (N. Y.), 188:5 (2013), 601–620

Citation in format AMSBIB
\Bibitem{Iva11}
\by S.~O.~Ivanov
\paper Selfinjective algebras of stable Calabi--Yau dimension three
\inbook Problems in the theory of representations of algebras and groups. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 394
\pages 226--261
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4636}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2870178}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 5
\pages 601--620
\crossref{https://doi.org/10.1007/s10958-013-1152-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884417616}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Ivanov, “$BV$-algebra structure on Hochschild cohomology of local algebras of quaternion type in characteristic 2”, J. Math. Sci. (N. Y.), 219:3 (2016), 427–461  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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