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$Z_{2}$ -graded extensions of the orthogonal Lie algebras

Hasiewicz, Zbigniew (1984)

Proceedings of the 12th Winter School on Abstract Analysis

Zero divisors in amalgamated free products of Lie algebras.

Chirkov, I.V., Shevelin, M.A. (2004)

Sibirskij Matematicheskij Zhurnal

Zeros of polynomials with coefficients in the center of a division algebra.

F. Leon Pritchard (1986/1987)

Manuscripta mathematica

Zeta functions of Jordan algebras representations

Dehbia Achab (1995)

Annales de l'institut Fourier

This work is about a generalization of Kœcher’s zeta function. Let $V$ be an Euclidean simple Jordan algebra of dimension $n$ and rank $m$ , $E$ an Euclidean space of dimension $N$ , $ϕ$ a regular self-adjoint representation of $V$ in $E$ , $Q$ the quadratic form associated to $ϕ$ , $Ω$ the symmetric cone associated to $V$ and $G (Ω)$ its automorphism group $G (Ω) = {g \in G L (V) | g (Ω) = Ω} .$ ( $H_{1}$ ) Assume that $V$ and $E$ have $Q$ -structures $V_{Q}$ and $E_{Q}$ respectively and $ϕ$ is defined over $Q$ . Let $L$ be a lattice in $E_{Q}$ . The zeta series associated to $ϕ$ and $L$ is defined by $ζ_{L} (s) = \sum_{l \in Γ_{\circ} ∖ L^{'}} [\det (Q (l))]^{- s}, \forall s \in C$ where $L^{'} = {l \in L | \det (Q (l)) \neq 0}$ ,...