On the q-exponential of matrix q-Lie algebras

• Autorzy: Thomas Ernst
• Języki publikacji: EN

Abstrakty

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 r, 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 × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant 1. The corresponding matrix multiplication is twisted under τ, 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 suq(4), and its corresponding q-Lie group. We conclude with an example of system of equations with Ward number coeficients.

Słowa kluczowe

EN

Ring morphism; q-determinant; Nova q-addition; q-exponential function; q-Lie algebra; q-trace; biring

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 36-50

Daty

wydano

2017-01-01

otrzymano

2016-07-04

zaakceptowano

2016-09-27

online

2017-01-20

Twórcy

autor

Thomas Ernst

• Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06 Uppsala,

Identyfikatory

DOI

10.1515/spma-2017-0003