Shift associative algebras
Abdelwahab H. Kaygorodov I. Sartayev B.
August 2025Springer-Verlag Italia s.r.l.
Rendiconti del Circolo Matematico di Palermo
2025#74Issue 5
We present a comprehensive study of algebras satisfying the identity (xy)z=y(zx), named as shift associative algebras. Our research shows that these algebras are related to many interesting identities. In particular, they are related to anti-Poisson-Jordan algebras and algebras of associative type σ. We study algebras of associative type σ to be Koszul and self-dual. A basis of the free shift associative algebra generated by a countable set X is constructed. An analog of Wedderburn-Malcev’s theorem is established. The algebraic and geometric classifications of complex 4-dimensional shift associative algebras are given. In particular, we prove that the first non-associative shift associative algebra appears only in dimension 5.
Algebraic classification , Free algebra , Geometric classification , Operads , Shift associative algebra
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Department of Mathematics, Mansoura University, Mansoura, Egypt
CMA-UBI, University of Beira Interior, Covilhã, Portugal
Narxoz University, Almaty, Kazakhstan
Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
Department of Mathematics
CMA-UBI
Narxoz University
Moscow Center for Fundamental and Applied Mathematics
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