The multiplicative Lie algebra on general linear groups
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Akshay Kumar
Abstract
The main aim of this paper is to study an obvious linear representation of a multiplicative Lie algebra. Also, we find some criteria to determine all possible multiplicative Lie algebra structures on a general linear group and we show that the general linear group on a finite field is a Lie simple group.
Funding statement: The second named author is thankful to IIIT Allahabad for providing SEED grant. The third named author is thankful to National Board of Higher Mathematics, Government of India (NBHM) for the financial support for the project entitled “Linear Representation of Multiplicative Lie Algebra” (02011/19/2023/NBHM/R & D-II/5954).
Acknowledgements
We are extremely thankful to Professor Ramji Lal for his continuous support, discussion and encouragement.
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Some results in prime rings involving endomorphisms
- On the generalized fractional Laplace–Bessel operator
- Smoothness of solutions of differential equations of constant strength in Roumieu spaces
- Rings additively generated by certain periodic elements
- Rings whose clean elements are uniquely strongly clean
- New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
- On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
- Characterization of multiplicative Jordan n-higher derivations on unital rings
- The multiplicative Lie algebra on general linear groups
- The optimal control problem for systems of integro-differential equations with finite and infinite horizon
- Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
- Nonlinear mixed Jordan-type derivations on *-algebras
- SG pseudo-differential operators in Dunkl setting
- Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
- The binary products of algebras with genetic realization
-
A relationship between the structure of a quotient ring and
Artikel in diesem Heft
- Frontmatter
- Some results in prime rings involving endomorphisms
- On the generalized fractional Laplace–Bessel operator
- Smoothness of solutions of differential equations of constant strength in Roumieu spaces
- Rings additively generated by certain periodic elements
- Rings whose clean elements are uniquely strongly clean
- New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
- On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
- Characterization of multiplicative Jordan n-higher derivations on unital rings
- The multiplicative Lie algebra on general linear groups
- The optimal control problem for systems of integro-differential equations with finite and infinite horizon
- Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
- Nonlinear mixed Jordan-type derivations on *-algebras
- SG pseudo-differential operators in Dunkl setting
- Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
- The binary products of algebras with genetic realization
-
A relationship between the structure of a quotient ring and
