Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities

I. generalizations of the Capelli and Turnbull identities

Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)1-43
    Number of pages43
    JournalElectronic Journal of Combinatorics
    Volume16
    Issue number1
    StatePublished - Aug 7 2009

    Fingerprint

    Capelli Identity
    Classical Invariant Theory
    Electric commutators
    Antisymmetric
    Commutator
    Cauchy
    Manipulation
    Determinant
    Generalization

    Keywords

    • 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

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Geometry and Topology
    • Theoretical Computer Science

    Cite this

    Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities : I. generalizations of the Capelli and Turnbull identities. / Caracciolo, Sergio; Sokal, Alan D.; Sportiello, Andrea.

    In: Electronic Journal of Combinatorics, Vol. 16, No. 1, 07.08.2009, p. 1-43.

    Research output: Contribution to journalArticle

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