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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Generalization of connection based on the concept of graded q-differential algebra; pp. 256–264

(Full article in PDF format) doi: 10.3176/proc.2010.4.02


Authors

Viktor Abramov, Olga Liivapuu

Abstract

We propose a generalization of the concept of connection form by means of a graded q-differential algebra Ωq, where q is a primitive Nth root of unity, and develop the concept of curvature N-form for this generalization of the connection form. The Bianchi identity for a curvature N-form is proved. We study an Ωq-connection on module and prove that every projective module admits an Ωq-connection. If the module is equipped with a Hermitian structure, we introduce a notion of an Ωq-connection consistent with the Hermitian structure.

Keywords

q-connection on module, connection form, covariant N-differential, Hermitian connection, Hermitian module, generalized cohomologies, N-complex.

References

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Current Issue: Vol. 68, Issue 2, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December