Search results for "Symmetric polynomial"

showing 2 items of 12 documents

Some algebras of symmetric analytic functions and their spectra

2011

AbstractIn the spectrum of the algebra of symmetric analytic functions of bounded type on ℓp, 1 ≤ p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the ‘radius’ function. It is also proved that the algebra of analytic functions of bounded type on ℓ1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of ℓ1. We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.

Pure mathematicsTriple systemGeneral MathematicsFreudenthal magic squareElementary symmetric polynomialStanley symmetric functionComplete homogeneous symmetric polynomialRing of symmetric functionsAlgorithmSymmetric closureMathematicsAnalytic functionProceedings of the Edinburgh Mathematical Society
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A Leibniz variety with almost polynomial growth

2005

Abstract Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V ˜ 1 defined by the identity y 1 ( y 2 y 3 ) ( y 4 y 5 ) ≡ 0 . We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety V ˜ 1 has almost polynomial growth, i.e., the sequence of codimensions of V ˜ 1 cannot be bounded by any polynomial function but any proper subvariety of V ˜ 1 as polynomial growth.

symbols.namesakePure mathematicsAlgebra and Number TheoryInvariant polynomialSymmetric polynomialAlternating polynomialLeibniz formula for determinantsHomogeneous polynomialsymbolsElementary symmetric polynomialPolarization of an algebraic formMathematicsSquare-free polynomialJournal of Pure and Applied Algebra
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