Open AccessSymmetric bi-derivations and their generalizations on group algebras
Author(s) -
Mohammad Gandomani Hossein,
Mohammad Mehdipour Javad
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.