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.12223
Inner 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.