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Search Results: 1 - 10 of 593180 matches for " L. A. Bokut "
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Groebner-Shirshov basis for the braid group in the Artin-Garside generators
L. A. Bokut
Mathematics , 2008,
Abstract: In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ in the Artin--Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup $B^+{n+1}$ is the subsemigroup in $B_{n+1}$.
Groebner-Shirshov basis for the braid group in the Birman-Ko-Lee-Garside generators
L. A. Bokut
Mathematics , 2008,
Abstract: In this paper, we obtain Groebner-Shirshov (non-commutative Gr\"obner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new ``Garside word" $\delta$. It gives a new algorithm for getting the Birman-Ko-Lee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.
Groebner-Shirshov Bases for Lie Algebras: after A. I. Shirshov
L. A. Bokut,Yuqun Chen
Mathematics , 2008,
Abstract: In this paper, we review Shirshov's method for free Lie algebras invented by him in 1962 which is now called the Groebner-Shirshov bases theory.
Groebner-Shirshov Bases: Some New Results
L. A. Bokut,Yuqun Chen
Mathematics , 2008,
Abstract: In this survey article, we report some new results of Groebner-Shirshov bases, including new Composition-Diamond lemmas, applications of some known Composition-Diamond lemmas and content of some expository papers.
Gr?bner-Shirshov bases and their calculation
L. A. Bokut,Yuqun Chen
Mathematics , 2013, DOI: 10.1007/s13373-014-0054-6
Abstract: In this survey, we formulate the Gr\"{o}bner-Shirshov bases theory for associative algebras and Lie algebras. Some new Composition-Diamond lemmas and applications are mentioned.
Gr?bner-Shirshov bases and PBW theorems
L. A. Bokut,Yuqun Chen
Mathematics , 2014,
Abstract: We review some applications of Gr\"obner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.
Composition-Diamond Lemma for Tensor Product of Free Algebras
L. A. Bokut,Yuqun Chen,Yongshan Chen
Mathematics , 2008, DOI: 10.1016/j.jalgebra.2010.02.021
Abstract: In this paper, we establish Composition-Diamond lemma for tensor product $k< X> \otimes k< Y>$ of two free algebras over a field. As an application, we construct a Groebner-Shirshov basis in $k< X> \otimes k< Y>$ by lifting a Groebner-Shirshov basis in $k[X] \otimes k< Y>$, where $k[X]$ is a commutative algebra.
Groebner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras
L. A. Bokut,Yuqun Chen,Jianjun Qiu
Mathematics , 2008,
Abstract: In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Groebner-Shirshov bases of free Rota-Baxter algebra, $\lambda$-differential algebra and $\lambda$-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar to those obtained by Ebrahimi-Fard and Guo, and Guo and Keigher recently by using other methods.
Groebner-Shirshov bases for dialgebras
L. A. Bokut,Yuqun Chen,Cihua Liu
Mathematics , 2008, DOI: 10.1142/S0218196710005753
Abstract: In this paper, we define the Gr\"obner-Shirshov basis for a dialgebra. The Composition-Diamond lemma for dialgebras is given then. As results, we give Gr\"obner-Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.
Groebner-Shirshov bases for free inverse semigroups
L. A. Bokut,Yuqun Chen,Xiangui Zhao
Mathematics , 2008,
Abstract: A new construction of a free inverse semigroup was obtained by Poliakova and Schein in 2005. Based on their result, we find a Groebner-Shirshov basis of a free inverse semigroup relative to the deg-lex order of words. In particular, we give the (unique and shortest) Groebner-Shirshov normal forms in the classes of equivalent words of a free inverse semigroup together with the Groebner-Shirshov algorithm to transform any word to its normal form.
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