Search results for " 15A72"

showing 2 items of 2 documents

Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras

2012

The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.

Classical Invariant Theory05A15 05E05 05E10 13A50 15A72 16R10 16R30 20G05MacMahon Partition AnalysisHilbert SeriesRational symmetric functions classical invariant theory algebras with polynomial identity cocharacter sequenceMathematics - Rings and AlgebrasCommutative Algebra (math.AC)Mathematics - Commutative AlgebraRational Symmetric FunctionsAlgebras with Polynomial IdentitySettore MAT/02 - AlgebraRings and Algebras (math.RA)Noncommutative Invariant TheoryFOS: MathematicsCocharacter SequenceMathematics - CombinatoricsCombinatorics (math.CO)
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Jordan Decompositions of Tensors

2022

We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra which acts on it and embed them into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information.

Mathematics - Algebraic GeometryMathematics::Rings and Algebras81P18 15A69 15A72FOS: Mathematics[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]Algebraic Geometry (math.AG)[PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]
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