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- W2014704189 abstract "In the context of the integration over algebras introduced in a previous paper, we obtain several results for a particular class of associative algebras with identity. The algebras of this class are called self-conjugated, and they include, for instance, the para-Grassmann algebras of order p, the quaternionic algebra and the toroidal algebras. We study the relation between derivations and integration, proving a generalization of the standard result for the Riemann integral about the translational invariance of the measure and the vanishing of the integral of a total derivative (for convenient boundary conditions). We consider also the possibility, given the integration over an algebra, to define from it the integral over a subalgebra, in a way similar to the usual integration over manifolds. That is by projecting out the submanifold in the integration measure. We prove that this is possible for para-Grassmann algebras of order p, once we consider them as subalgebras of the algebra of the (p + 1) × (p + 1) matrices. We find also that the integration over the subalgebra coincides with the integral defined in the direct way. As a by-product we can define the integration over a one-dimensional Grassmann algebra as a trace over 2 × 2 matrices." @default.
- W2014704189 created "2016-06-24" @default.
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- W2014704189 date "1998-12-30" @default.
- W2014704189 modified "2023-10-14" @default.
- W2014704189 title "ALGEBRAS, DERIVATIONS AND INTEGRALS" @default.
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- W2014704189 doi "https://doi.org/10.1142/s0217751x98002481" @default.
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