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Universal Algebra Applied to Hom-Associative Algebras, and More

The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we review the main results. We discuss the envelopment problem, operads, and the Diamond Lemma; the usual tools have to be adapted to this new situation. Moreover we study Hilbert series for the hom-associative operad and free algebra, and describe them up to total degree equal 8 and 9 respectively.

preprint2014arXivOpen access
Lars HellströmAbdenacer MakhloufSergei D. Silvestrov
math.RA
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Open access3 authors1 topic
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Lars HellströmAbdenacer MakhloufSergei D. Silvestrov

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