Author: "Mikhail Kochetov" / Language: english - Searchworks@Jio Institute Digital Library Search Results

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Author: Adrián Rodrigo-Escudero, Yuri Bahturin, and Mikhail Kochetov
Subjects: Pure mathematics, Algebra and Number Theory, Simple Lie group, 010102 general mathematics, Non-associative algebra, 17B70 (Primary), 16W50, 16W10 (Secondary), Real form, 010103 numerical & computational mathematics, Mathematics - Rings and Algebras, Killing form, 01 natural sciences, Affine Lie algebra, Adjoint representation of a Lie algebra, Representation of a Lie group, Rings and Algebras (math.RA), FOS: Mathematics, Fundamental representation, 0101 mathematics, Mathematics
Abstract: For any abelian group $G$, we classify up to isomorphism all $G$-gradings on the classical central simple Lie algebras, except those of type $D_4$, over the field of real numbers (or any real closed field)., 35 pages
Published: 2017

Author: Mikhail Kochetov, Helen Samara Dos Santos, and Caio De Naday Hornhardt
Subjects: Algebra and Number Theory, Mathematics::Commutative Algebra, 010102 general mathematics, Mathematics::Rings and Algebras, Lie superalgebra, Mathematics - Rings and Algebras, 16. Peace & justice, 01 natural sciences, Combinatorics, Rings and Algebras (math.RA), Mathematics::Quantum Algebra, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, 0101 mathematics, Abelian group, Algebraically closed field, Mathematics::Representation Theory, 17B70 (Primary) 16W50, 16W55, 17A70 (Secondary), Mathematics
Abstract: We classify gradings by arbitrary abelian groups on the classical simple Lie superalgebras $P(n)$, $n \geq 2$, and on the simple associative superalgebras $M(m,n)$, $m, n \geq 1$, over an algebraically closed field: fine gradings up to equivalence and $G$-gradings, for a fixed group $G$, up to isomorphism. As a corollary, we also classify up to isomorphism the $G$-gradings on the classical Lie superalgebra $A(m,n)$ that are induced from $G$-gradings on $M(m+1,n+1)$. In the case of Lie superalgebras, the characteristic is assumed to be $0$., 29 pages
Published: 2017

Author: Alberto Elduque and Mikhail Kochetov
Subjects: 010102 general mathematics, 0103 physical sciences, Mathematics::Rings and Algebras, FOS: Mathematics, 010307 mathematical physics, 16W50 (Primary), 17B70 (Secondary), 0101 mathematics, Representation Theory (math.RT), 01 natural sciences, Mathematics - Representation Theory
Abstract: Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be isomorphic to each other. Under some restrictions, these loop modules are completely reducible (as ungraded modules), and some of their invariants --- inertia group, graded Brauer invariant and Schur index --- which were previously defined for simple modules over graded finite-dimensional semisimple Lie algebras over an algebraically closed field of characteristic zero, are now considered in a more general and natural setting., 30 pages; some explanatory remarks are added in this version
Published: 2016

Author: Mikhail Kochetov and Oana Radu
Abstract: Abstract We prove analogues of the classical Engel’s Theorem for Lie algebras in the category of comodules over a cotriangular Hopf algebra, generalizing the known result for Lie coloralgebras. [ABSTRACT FROM AUTHOR]
Published: 2010
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Author: Mikhail Kochetov and Michael Slawinski
Subjects: ELASTICITY, PROPERTIES of matter, MATHEMATICAL physics, MATHEMATICAL analysis
Abstract: Abstract We consider the problem of finding the transversely isotropic elasticity tensor closest to a given elasticity tensor with respect to the Frobenius norm. A similar problem was considered by other authors and solved analytically assuming a fixed orientation of the natural coordinate system of the transversely isotropic tensor. In this paper we formulate a method for finding the optimal orientation of the coordinate system—the one that produces the shortest distance. The optimization problem reduces to finding the absolute maximum of a homogeneous eighth-degree polynomial on a two-dimensional sphere. This formulation allows us a convenient visualization of local extrema, and enables us to find the closest transversely isotropic tensor numerically. [ABSTRACT FROM AUTHOR]
Published: 2009
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Author: Yuri Bahturin, Mikhail Kochetov, and Susan Montgomery
Subjects: *LIE algebras, *ABELIAN groups, *FINITE groups, *ALGEBRAIC fields, *DIVISIBILITY groups, *MATHEMATICS
Abstract: In this paper we describe all gradings by a finite abelian group $G$ on the following Lie algebras over an algebraically closed field $F$ of characteristic $pneq 2$: $mathfrak {sl}_n(F)$ ($n$ not divisible by $p$), $mathfrak {so}_n(F)$ ($ngeq 5$, $nneq 8$) and $mathfrak {sp}_n(F)$ ($ngeq 6$, $n$ even). [ABSTRACT FROM AUTHOR]
Published: 2008
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Author: Jakob Cimpri?, Mikhail Kochetov, and Murray Marshall
Abstract: Abstract?? Our aim is to construct new examples of totally ordered and ?-ordered noncommutative integral domains. We will discuss the following classes of rings: enveloping algebrasU(L), group rings $"$\bbbk$"$ Gand smash productsU(L) $"$\#$ G. All of them are examples of Hopf algebras. Characterizations of orderability for enveloping algebras and group rings and of ?-orderability for enveloping algebras have been found before and will be recalled in the article. Our main results are: for $"$\bbbk$ andLfinite?dimensional, we characterize the orderability ofU(L) $"$\#$ G; for $"$\bbbk$ , we give a necessary and a sufficient condition for ?-orderability of $"$\bbbk$"$ G(Gorderable, respectively,Gresidually ?torsion-free nilpotent?). Moreover, for $"$\bbbk$ andLfinite-dimensional, we reduce the problem of characterizing the ?-orderability ofU(L) $"$\#$ Gto the problem of characterizing the ?-orderability of $"$\bbbk$"$ G. The latter remains open. [ABSTRACT FROM AUTHOR]
Published: 2007
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