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On the q-exponential of matrix q-Lie algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2017 (English)In: Special Matrices, ISSN 2300-7451, Vol. 5, no 1, p. 36-50Article in journal (Refereed) Published
Abstract [en]

In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus. We first introduce the ring epimorphism tau, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n x n matrix, a so-called q-Lie group, or manifold, usually with q-determinant 1. The corresponding matrix multiplication is twisted under tau, which makes it possible to draw diagrams similar to Lie group theory for the q-exponential, or the so-called q-morphism. There is no definition of letter multiplication in a general alphabet, but in this article we introduce new q-number systems, the biring of q-integers, and the extended q-rational numbers. Furthermore, we provide examples of matrices in su(q)(4), and its corresponding q-Lie group. We conclude with an example of system of equations with Ward number coeficients.

Place, publisher, year, edition, pages
2017. Vol. 5, no 1, p. 36-50
Keywords [en]
Ring morphism, q-determinant, Nova q-addition, q-exponential function, q-Lie algebra, q-trace, biring
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-340171DOI: 10.1515/spma-2017-0003ISI: 000413784000002OAI: oai:DiVA.org:uu-340171DiVA, id: diva2:1178680
Available from: 2018-01-30 Created: 2018-01-30 Last updated: 2018-01-30Bibliographically approved

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