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Sibirsk. Mat. Zh., 2013, Volume 54, Number 5, Pages 1128–1149 (Mi smj2482)  

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

Lie algebras in symmetric monoidal categories

D. A. Rumynin

Department of Mathematics, University of Warwick, Coventry, CV4 7AL, UK

Abstract: We study the algebras that are defined by identities in the symmetric monoidal categories; in particular, the Lie algebras. Some examples of these algebras appear in studying the knot invariants and the Rozansky–Witten invariants. The main result is the proof of the Westbury conjecture for a K3-surface: there exists a homomorphism from a universal simple Vogel algebra into a Lie algebra that describes the Rozansky–Witten invariants of a K3-surface. We construct a language that is necessary for discussing and solving this problem, and we formulate nine new problems.

Keywords: tensor category, Lie algebra, K3-surface, Rozansky–Witten invariants.

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English version:
Siberian Mathematical Journal, 2013, 54:5, 905–921

Bibliographic databases:

UDC: 512.554
Received: 16.05.2012

Citation: D. A. Rumynin, “Lie algebras in symmetric monoidal categories”, Sibirsk. Mat. Zh., 54:5 (2013), 1128–1149; Siberian Math. J., 54:5 (2013), 905–921

Citation in format AMSBIB
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\pages 1128--1149
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\vol 54
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\pages 905--921
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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. R. L. Mkrtchyan, “On universal quantum dimensions”, Nucl. Phys. B, 921 (2017), 236–249  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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