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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 3, Pages 131–158 (Mi izv8251)  

This article is cited in 11 scientific papers (total in 11 papers)

Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero

S. V. Pchelintseva, O. V. Shashkovb

a Financial University under the Government of the Russian Federation, Moscow
b Moscow State Regional Institute of Humanities

Abstract: We classify simple finite-dimensional right-alternative superalgebras $A=A_0\oplus A_1$ over a field of characteristic zero in which the even part $A_0$ is associative and commutative, while $A_1$ is an associative $A_0$-bimodule. We prove that every such superalgebra $A=A_0\oplus A_1$ is obtained by doubling the semisimple even part $A_0$, and the multiplication in $A$ is defined using a suitable automorphism and a linear operator acting on $A_0$.

Keywords: simple superalgebra, right-alternative superalgebra.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00014
This research was supported by the Russian Foundation for Basic Research (grant no. 14-01-00014).


DOI: https://doi.org/10.4213/im8251

Full text: PDF file (630 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:3, 554–580

Bibliographic databases:

UDC: 512.554.5
MSC: 17A70, 17D15, 17D05
Received: 13.05.2014

Citation: S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero”, Izv. RAN. Ser. Mat., 79:3 (2015), 131–158; Izv. Math., 79:3 (2015), 554–580

Citation in format AMSBIB
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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. S. V. Pchelintsev, O. V. Shashkov, “Simple Finite-Dimensional Right Alternative Superalgebras with Unitary Even Part over a Field of Characteristic $0$”, Math. Notes, 100:4 (2016), 589–596  mathnet  crossref  crossref  mathscinet  isi  elib
    2. S. V. Pchelintsev, O. V. Shashkov, “Simple right alternative superalgebras of Abelian type whose even part is a field”, Izv. Math., 80:6 (2016), 1231–1241  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. N. Zhelyabin, “Simple Jordan superalgebras with associative nil-semisimple even part”, Siberian Math. J., 57:6 (2016), 987–1001  mathnet  crossref  crossref  isi  elib
    4. S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative superalgebras with semisimple strongly associative even part”, Sb. Math., 208:2 (2017), 223–236  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part”, Sb. Math., 208:4 (2017), 531–545  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. S. V. Pchelintsev, O. V. Shashkov, “Simple $5$-dimensional right alternative superalgebras with trivial even part”, Siberian Math. J., 58:6 (2017), 1078–1089  mathnet  crossref  crossref  isi  elib
    7. S. V. Pchelintsev, O. V. Shashkov, “Singulyarnye 6-mernye superalgebry”, Sib. elektron. matem. izv., 15 (2018), 92–105  mathnet  crossref
    8. S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative unital superalgebras with associative-commutative even part over a field of characteristic zero”, Izv. Math., 82:3 (2018), 578–595  mathnet  crossref  crossref  adsnasa  isi  elib
    9. V. N. Zhelyabin, “Structure of some unital simple Jordan superalgebras with associative even part”, Siberian Math. J., 59:6 (2018), 1051–1062  mathnet  crossref  crossref  isi  elib
    10. S. V. Pchelintsev, O. V. Shashkov, “Prostye unitalnye pravoalternativnye superalgebry nad algebroi matrits poryadka $2$”, Algebra i logika, 58:1 (2019), 108–131  mathnet  crossref
    11. S. V. Pchelintsev, O. V. Shashkov, “Prostye asimmetrichnye dubli, ikh avtomorfizmy i differentsirovaniya”, Algebra i logika, 58:5 (2019), 627–649  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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