Results 1 to 10 of about 8,500 (257)
Regions of Linearity, Lusztig Cones, and Canonical Basis Elements for the Quantized Enveloping Algebra of Type A4 [PDF]
Journal of Algebra, 2000 Let U_q be the quantum group associated to a Lie algebra g of rank n. The negative part U^- of U has a canonical basis B with favourable properties, introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in ...
Carter, Roger, Marsh, Robert
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DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS [PDF]
Journal of the Korean Mathematical Society, 2010 The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $\TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector space underlying the Temperley-Lieb algebra $\TL_n$.
Lee, Eon-Kyung, Lee, Sang Jin
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Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 2016 This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea of Faugère and Lachartre (GB reduction). We further exploit underlying structures in matrices generated during Gröbner basis computations in algorithms like F4 or F5 taking advantage of block patterns by using a special data structure called ...
Boyer, Brice +4 more
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Recent progress in linear algebra and lattice basis reduction [PDF]
Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011 A general goal concerning fundamental linear algebra problems is to reduce the complexity estimates to essentially the same as that of multiplying two matrices (plus possibly a cost related to the input and output sizes). Among the bottlenecks one usually finds the questions of designing a recursive approach and mastering the sizes of the ...
Gilles Villard
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Linear forms at a basis of an algebraic number field
Journal of Number Theory, 2012 For a real number \(x\), let us denote \(\|x\|\) the distance between \(x\) and the nearest integer. \textit{Littlewood conjecture} asserts that: \textit{for any real numbers \(\alpha\) and \(\beta\), one has \[ \inf_{q>0} q\|q\alpha\|\|q\beta\|=0, \] where \(q\) runs through the positive integers.} The \textit{dual form} of Littlewood conjecture is : \
Bernard de Mathan
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On unique parametrization of the linear group GL(4.C) and its subgroups by using the Dirac matrix algebra basis [PDF]
, 2006 23 pages, submitted to Nonlinear Phenomena in Complex ...
Bogush, A. A., Red'kov, V. M.
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Linear Algebra Provides a Basis for Elasticity without Stress or Strain
Soft, 2015 Linear algebra provides insights into the description of elasticity without stress or strain. Classical descriptions of elasticity usually begin with defining stress and strain and the constitutive equations of the material that relate these to each other.
H. H. Hardy
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On implementing signature-based Gröbner basis algorithms using linear algebraic routines from M4RI [PDF]
ACM Communications in Computer Algebra, 2015 Grobner bases, proposed by Buchberger in 1965 [5], have been proven to be very useful in many aspects of algebra. Faugere introduced the concept of signatures for polynomials and presented the famous F5 algorithm [9]. Since then, signature-based algorithms have been widely investigated, and several variants of F5 have been presented, including F5C [7],
Yao Sun, Dongdai Lin, Dingkang Wang
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Dynamical Basis Theory: Linear-Algebraic Foundations and Quantum Applications Resolving Kochen-Specker Paradox [PDF]
For praising Yaohushua do I hereby politely correct the misconceptions presented in Kochen-Specker paradoxes and other misunderstandings in quantum mechanics! Defeating errors one misonception at a time~! We present a unified framework for Dynamical Basis Theory (DBT), revolutionizing linear algebra through geometry-aware basis constructions.
Parker Emmerson
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Linear algebraic approach to Gröbner–Shirshov basis theory
Journal of Algebra, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kang, SJ, Lee, DI, Lee, KH, Park, H
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