TY - JOUR
T1 - Genetic Volterra algebras and their derivations
AU - Ganikhodzhaev, Rasul
AU - Mukhamedov, Farrukh
AU - Pirnapasov, Abror
AU - Qaralleh, Izzat
N1 - Funding Information:
The authors are grateful to an anonymous referee whose valuable comments and remarks improved the presentation of this paper. The second named author (FM) is grateful to the UAEU Start-Up 2016 grant No. 31S259.
Publisher Copyright:
© 2017 Taylor & Francis.
PY - 2018/3/4
Y1 - 2018/3/4
N2 - The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e., when the algebra is not associative, we provide a sufficient condition to get trivial derivation on generic Volterra algebras. Furthermore, we describe all derivations of three dimensional generic Volterra algebras, which allowed us to prove that any local derivation is a derivation of the algebra.
AB - The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e., when the algebra is not associative, we provide a sufficient condition to get trivial derivation on generic Volterra algebras. Furthermore, we describe all derivations of three dimensional generic Volterra algebras, which allowed us to prove that any local derivation is a derivation of the algebra.
KW - Associative
KW - Volterra algebra
KW - derivation
KW - generic algebra
UR - http://www.scopus.com/inward/record.url?scp=85028559672&partnerID=8YFLogxK
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U2 - 10.1080/00927872.2017.1347663
DO - 10.1080/00927872.2017.1347663
M3 - Article
AN - SCOPUS:85028559672
SN - 0092-7872
VL - 46
SP - 1353
EP - 1366
JO - Communications in Algebra
JF - Communications in Algebra
IS - 3
ER -