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Gröbner–Shirshov bases for pre-associative algebras

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0 Published in 2017 at "Communications in Algebra"

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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1 Published in 2017 at "Communications in Algebra"

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 symmetric brace algebras

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1 Published in 2020 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1821699

Abstract: Abstract In this paper, we develop Gröbner–Shirshov basis theory for symmetric brace algebras. As applications, firstly, we give an alternative proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie… read more here.

Keywords: symmetric brace; bner shirshov; lie algebra; pre lie ... See more keywords

Gröbner–Shirshov Bases for Replicated Algebras

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0 Published in 2017 at "Algebra Colloquium"

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

Gröbner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups

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0 Published in 2018 at "Symmetry"

DOI: 10.3390/sym10100438

Abstract: We construct a Gröbner-Shirshov basis of the Temperley-Lieb algebra T (d, n) of the complex reflection group G(d, 1, n), inducing the standard monomials expressed by the generators {Ei} of T (d, n). This result… read more here.

Keywords: complex reflection; temperley lieb; bner shirshov; reflection group ... See more keywords