Akademik Veri Yönetim Sistemi
Ricerche di Matematica, 2025 (SCI-Expanded)
An algebra is bicommutative if it satisfies left and right symmetries; i.e., a(bc)=b(ac) and (ab)c=(ac)b. Let K be a field of characteristic zero, and Mn, n≥3, be the free metabelian bicommutative algebra generated by a set Xn={x1,…,xn} of variables, in which the identity (xy)(zt)=0 is being satisfied. We define the action of the alternating group An on Mn as follows. πf(x1,…,xn)=f(xπ(1),…,xπ(n)), where π∈An and f∈Mn. The set MnAn={f∈Mn∣πf=f,∀π∈An} is a subalgebra of Mn called the algebra of invariants of the group An. In the first part of this study, we describe the elements of the algebra MnAn. We also give the description of the algebras M2C2, M2C3, M2C2×C2, and M2C4 of invariants of the groups C2, C3, C2×C2, and C4 of order up to 4, respectively, as a subgroups of the general linear group GL2(K).