Shift associative algebras
Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev

TL;DR
This paper introduces and studies shift associative algebras, exploring their properties, classifications, and relations to other algebraic structures, including their basis, duality, and dimensional characteristics.
Contribution
It provides a comprehensive analysis of shift associative algebras, including their basis, classification, and connections to other algebraic systems, with new results on their structure and dimensionality.
Findings
Constructed a basis for free shift associative algebra.
Established an analog of Wedderburn-Artin's theorem.
Classified complex 4-dimensional shift associative algebras.
Abstract
We present a comprehensive study of algebras satisfying the identity 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 . We study algebras of associative type to be Koszul and self-dual. A basis of the free shift associative algebra generated by a countable set was constructed. An analog of Wedderburn-Artin's theorem was established. The algebraic and geometric classifications of complex -dimensional shift associative algebras are given. In particular, we proved that the first non-associative shift associative algebra appears only in dimension .
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Rings, Modules, and Algebras
