In this paper we study complexes of $k$ Dirac operators (or variations of Dirac operators) in the real or complex Clifford algebras $\cc_m$ i.e. complexes in which the first map is induced by the matrix $[\pp_{\ux_1},\ldots ,\pp_{\ux_k}]$ where $\pp_{\ux_i}$ is the Dirac operator with respect to the variable $x_i\in\cc_m$. In particular we prove that, if $m\geq 5$, the complex in the case of $3$ operators can be described in terms of relations coming from the so called {\em radial algebra}. Moreover we show that if the dimension $m$ is less than $2k-1$, then the Fischer decomposition does not hold.
Complexes of Dirac Operators in Clifford Algebras
SABADINI, IRENE MARIA;
2002-01-01
Abstract
In this paper we study complexes of $k$ Dirac operators (or variations of Dirac operators) in the real or complex Clifford algebras $\cc_m$ i.e. complexes in which the first map is induced by the matrix $[\pp_{\ux_1},\ldots ,\pp_{\ux_k}]$ where $\pp_{\ux_i}$ is the Dirac operator with respect to the variable $x_i\in\cc_m$. In particular we prove that, if $m\geq 5$, the complex in the case of $3$ operators can be described in terms of relations coming from the so called {\em radial algebra}. Moreover we show that if the dimension $m$ is less than $2k-1$, then the Fischer decomposition does not hold.File in questo prodotto:
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