Results 1 to 10 of about 88,077 (185)
Polynomial identities for hypermatrices
, 2002 We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.Comment: 65 pages. Several results expanded.
Tapia, Victor
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Multialternating graded polynomials and growth of polynomial identities [PDF]
Proceedings of the American Mathematical Society, 2012 Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large ...
Aljadeff, Eli, Giambruno, Antonio
core +3 more sources
Algebras, dialgebras, and polynomial identities [PDF]
, 2012 This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations.
Bremner, Murray R.
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Tensor polynomial identities [PDF]
Israel Journal of Mathematics, 2021 Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their associated Young tableaux.
Huber, Felix, Procesi, Claudio
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Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]
, 2017 In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
Odake, Satoru
core +3 more sources
Knot polynomial identities and quantum group coincidences [PDF]
, 2011 We construct link invariants using the $D_{2n}$ subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also
Morrison, Scott +2 more
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Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras [PDF]
, 2013 We define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities ...
Kassel, Christian
core +5 more sources
A Penrose polynomial for embedded graphs [PDF]
, 2011 We extend the Penrose polynomial, originally defined only for plane graphs, to graphs embedded in arbitrary surfaces. Considering this Penrose polynomial of embedded graphs leads to new identities and relations for the Penrose polynomial which can not be
Aigner +22 more
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Polynomial identities on eigenforms
Journal of Number Theory, 2016 In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL2(Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases, only finitely many such identities hold for a fixed polynomial.
Richey, Joseph, Shutty, Noah
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Superalgebras: Polynomial identities and asymptotics
Journal of Algebra, 2022 Let \(A\) be an associative superalgebra, one attaches to it the \textit{sequence of supercodimensions} \(c_n^{\sup}(A)\), \(n \ge1\). In case of characteristic zero, it is well known that for a PI-superalgebra such a sequence is exponentially bounded, and the limit \(\exp^{\sup}(A) = \lim_{n\to\infty}\sqrt[n]{c_n^{\sup}(A)}\) exists and is an integer ...
Giambruno A., La Mattina D.
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