Symmetric bi-derivations and their generalizations on group algebras | Zendy

Mohammad Hossein Ahmadi Gandomani | Zendy; M. J. Mehdipour | Zendy

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Symmetric bi-derivations and their generalizations on group algebras

Author(s) -

Mohammad Hossein Ahmadi Gandomani,

M. J. Mehdipour

Publication year - 2021

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil2104233g

Subject(s) - mathematics , triple system , symmetric group , zero (linguistics) , group (periodic table) , combinatorics , symmetric closure , pure mathematics , algebra over a field , ring of symmetric functions , physics , quantum mechanics , philosophy , linguistics , orthogonal polynomials , difference polynomials

Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, we show that if B:L?0(G)*x L?0(G)* ? L?0(G)* is asymmetric bi-derivation such that [B(m,m),mk] ? Z(L?0(G)*) for all m ? L?0 (G)*, then B is the zero map. Furthermore, we characterize symmetric generalized biderivations on group algebras. We also prove that any symmetric Jordan bi-derivation on L? 0(G)* is a symmetric bi-derivation.

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