Computational Approach to Polynomial Identities of Matrices — a Survey

Benanti, Francesca

doi:10.1201/9780203911549.ch5

Cited by 11 publications

(11 citation statements)

References 52 publications

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“…The T -ideal of identities for M 2 (F) has been studied by many authors [42]. Computational methods used to study polynomial identities of matrices are discussed by Benanti et al [2]. Problem 2.13.…”

Section: Minimal Identitiesmentioning

confidence: 99%

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Bremner¹,

Madariaga²,

Peresi³

2017

Commentationes Mathematicae Universitatis Carolinae

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Section: Minimal Identitiesmentioning

confidence: 99%

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Bremner¹,

Madariaga²,

Peresi³

2017

Commentationes Mathematicae Universitatis Carolinae

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“…We point out that (the complements of) these computational problems arise in practice [BDDK03], hence their complexity is worthwhile investigating. Fact 4.10 carries over to the case of noncommutative ( * -) rings:…”

Section: Feasibility In Matrix Ringsmentioning

confidence: 99%

Computational Complexity of Quantum Satisfiability

Herrmann

Ziegler

2011

2011 IEEE 26th Annual Symposium on Logic in Computer Science

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Quantum logic generalizes, and in dimension one coincides with, Boolean propositional logic. We introduce the weak and strong satisfiability problem for quantum logic formulas; and show both 퓝 퓟-complete in dimension two as well. For higher-dimensional spaces ℝ and ℂ with ≥ 3 fixed, on the other hand, we show the problem to be complete for the nondeterministic Blum-Shub-Smale model of real computation. This provides a unified view on both Turing and real BSS complexity theory; and adds (a perhaps more natural and combinatorially flavoured) one to the still sparse list of 퓝 퓟ℝ-complete problems, mostly pertaining to real algebraic geometry. Our proofs rely on (a careful examination of) works by John von Neumann as well as contributions by Hagge et.al (2005,2007,2009). We finally investigate the problem over indefinite finite dimensions and relate it to noncommutative semialgebraic geometry.

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“…It would of course be interesting to relate our super identity with the general theory of PI-algebras (a very active domain, see e.g. [2,19,22]) where the classical Amitsur-Levitzki theorem plays an important role. That is a different study, which remains to be done since our super identity does not seem to appear in the PI-algebras literature.…”

Section: Comments and Perspectivesmentioning

confidence: 99%

THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA 𝔬𝔰𝔭(1, 2n)

Pinczon¹,

Ushirobira²

2006

J. Algebra Appl.

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Communicated by Ian M. MussonBased on Kostant's cohomological interpretation of the Amitsur-Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras osp(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur-Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.

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Computational Approach to Polynomial Identities of Matrices — a Survey

Cited by 11 publications

References 52 publications

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Computational Complexity of Quantum Satisfiability

THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA 𝔬𝔰𝔭(1, 2n)

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