Gröbner–Shirshov bases for pre-associative algebras
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DOI: 10.1080/00927872.2017.1304552
Abstract: ABSTRACT We develop Gröbner–Shirshov bases technique for pre-associative (dendriform) algebras and prove a version of composition-diamond lemma. read more here.
Keywords: bases pre; shirshov bases; pre associative; associative algebras ... See more keywords
Gröbner–Shirshov bases for brace algebras
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DOI: 10.1080/00927872.2018.1448846
Abstract: ABSTRACT Let A be a brace algebra. This structure implies that A is also a pre-Lie algebra. In this paper, we establish Composition-Diamond lemma for brace algebras. For each pre-Lie algebra L, we find a… read more here.
Keywords: shirshov bases; bases brace; bner shirshov; pre lie ... See more keywords
Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras
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DOI: 10.1142/s0219498817501900
Abstract: We generalize the Lyndon–Shirshov words to the Lyndon–Shirshov Ω-words on a set X and prove that the set of all the nonassociative Lyndon–Shirshov Ω-words forms a linear basis of the free Lie Ω-algebra on the… read more here.
Keywords: shirshov bases; lie; lie algebras; rota baxter ... See more keywords
Gröbner–Shirshov Bases for Replicated Algebras
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DOI: 10.1142/s1005386717000372
Abstract: We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner–Shirshov bases method for Lie algebras to solve the… read more here.
Keywords: algebra; shirshov bases; bases replicated; replicated algebras ... See more keywords