Volume 4 • Issue 2 • PP: 24-30 • 2023
A Representation of the Generators of the Quotients Group of Sl_2 By Matrices with Special Properties
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© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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The problem of the existence and construction of a resolution of singularities is one of the central questions of algebraic geometry. In this paper, we study this problem in connecting with the quotients for . It is known that the action of on its Lie algebra is corresponding to the action of on . As a result of this action, it will be an invariant ring, which determines the quotients for . This paper is devoted to studying the singularity of these quotients. We write this singularity as a matrix with interesting features such as, for example, its quadratic is a zero matrix and its rank is less than or equal to 1. Therefore, in this paper, we reduce the studying of the singularity of the quotients of , which is a hard problem, to the studying of a matrix of invariants which is an easy problem.
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References
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