Vladimir G. Tkachev
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Inner isotopes associated with automorphisms of commutative associative
algebras
cm:12223 -
Communications in Mathematics,
September 9, 2024,
Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
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https://doi.org/10.46298/cm.12223Inner isotopes associated with automorphisms of commutative associative
algebrasArticle
Authors: Vladimir G. Tkachev
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Vladimir G. Tkachev
The principal observation of the present paper is that an inner isotopy (i.e.
a principal isotopy defined by an algebra endomorphism) is a very helpful instrument in constructing and studying interesting classes of nonassociative algebras. By using methods developed in the paper, we define a new class of commutative nonassociative algebras obtained by inner isotopy from commutative associative polynomial algebras. There is a natural bijection between isomorphism classes of our algebras and integer partitions of the algebra dimensions. Among the interesting features of the nonassociative algebras constructed are that these algebras are generic, some of examples are axial and metrized algebras. We completely describe both the set of algebra idempotents and their spectra.
Volume: Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
Published on: September 9, 2024
Accepted on: July 26, 2024
Submitted on: September 1, 2023
Keywords: Mathematics - Rings and Algebras, Mathematics - Representation Theory, 12E05, 17A01