Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities
Copyright policy )Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities
We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy–Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull's Capelli-type identities for symmetric and antisymmetric matrices.
- University of Milan Italy
- New York University United States
- University College London United Kingdom
classical invariant theory, Determinants, permanents, traces, other special matrix functions, determinant, right-quantum matrix, permanent, Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), column-determinant, Turnbull identity, Weyl algebra, Representation Theory (math.RT), Combinatorial identities, bijective combinatorics, row-determinant, noncommutative determinant, representation theory, Mathematics - Rings and Algebras, Capelli identity, Capelli identity; Cauchy-binet theorem; Cayley identity; Classical invariant theory; Columndeterminant; Determinant; Noncommutative determinant; Noncommutative ring; Permanent; Representation theory; Row-determinant; Turnbull identity; Weyl algebra, Manin matrix, Rings and Algebras (math.RA), noncommutative ring, Combinatorics (math.CO), Cauchy-Binet theorem, Howe-Umeda-Kostant-Sahi identity, Cartier-Foata matrix, 15A15 (Primary), 05A19, 05A30, 05E15, 13A50, 15A24, 15A33, 15A72, 17B35, 20G05 (Secondary), Cayley identity, Mathematics - Representation Theory
classical invariant theory, Determinants, permanents, traces, other special matrix functions, determinant, right-quantum matrix, permanent, Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), column-determinant, Turnbull identity, Weyl algebra, Representation Theory (math.RT), Combinatorial identities, bijective combinatorics, row-determinant, noncommutative determinant, representation theory, Mathematics - Rings and Algebras, Capelli identity, Capelli identity; Cauchy-binet theorem; Cayley identity; Classical invariant theory; Columndeterminant; Determinant; Noncommutative determinant; Noncommutative ring; Permanent; Representation theory; Row-determinant; Turnbull identity; Weyl algebra, Manin matrix, Rings and Algebras (math.RA), noncommutative ring, Combinatorics (math.CO), Cauchy-Binet theorem, Howe-Umeda-Kostant-Sahi identity, Cartier-Foata matrix, 15A15 (Primary), 05A19, 05A30, 05E15, 13A50, 15A24, 15A33, 15A72, 17B35, 20G05 (Secondary), Cayley identity, Mathematics - Representation Theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).9 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!