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Two-parameter bicovariant differential calculi on F(R_q(1|1))

2018
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Advisor: Dr. Öğr. Üyesi Salih Çelik

Abstract (EN)

Supermatrices with complex entries act as linear transformations on complex spaces. Linear transformations that exist its inverse constitute a group. If we denote group of 2*2-supermatrices with GL(1|1), we consider the supermatrices belong this group as linear trasnformations of space R(1|1). One of the basic structure giving direction to the non-commutative supergeometry is to set up differential calculus on an associative superalgebra. It is constituted differantial calculi that left covariant with respect to supergroup GL_q(1|1) on coordinate algebra of Z_2-graded quantum plane. Differential calculus can be constituted on super-Hopf algebras, too. In this study, it will be constituted two 2-parameter differential calculi that bicovariant on algebra of functions on deformed superplane R_q(1|1) which is a super-Hopf algebra. After the obtaining 2-parameter deformations of supergroup GL(1|1), it will be shown that the differential calculi are left covariant with respect to super-Hopf algebra O(GL_p,q(1|1)).

Author

İlknur Temli

How to Cite

İlknur Temli (Master Thesis). Two-parameter bicovariant differential calculi on F(R_q(1|1)), 2018, Yıldız Technical University.

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