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Totally positive sequences andR-matrix quadratic algebras

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Abstract

Using the theory of Schur functions, we prove that the coefficients of the Hilbert series of a quadraticR-matrix algebra (for a Heckian R-matrix) form a totally positive sequence. The well-known description of the generation series for totally positive sequences implies that the Hilbert series of the quadratic R-matrix algebra is rational with real positive poles and real negative zeros. Using this characterization, we obtain the examples of Koszul and non-R-matrix algebras.

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Authors
  1. A. A. Davydov
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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 58, Algebra-12, 1998.

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Davydov, A.A. Totally positive sequences andR-matrix quadratic algebras. J Math Sci 100, 1871–1876 (2000). https://doi.org/10.1007/BF02677498

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