Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 11, 17 November 2023
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Exploring projective equivalences between closures of orbits
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Abstract
Motivated by results in the literature that use representations and group actions to produce nice geometric results about algebraic varieties, this article studies projective equivalence relations between closures of orbits for several complex algebraic group actions on , where is a complex representation of . In particular, we study the cases when is one of the following:, , , and . On the way, we also obtain some interesting geometric results from studying these orbits.
Keywords
projective equivalence, orbits, representations of algebraic groups.
References
1. Humphreys, J. E. (1995). Conjugacy Classes in Semisimple Algebraic Groups. American Mathematical Society.
2. He, X., Thomsen, J. F. (2006). Closures of Steinberg Fibers in Twisted Wonderful Compactifications. Transformations Groups, 11(3), 427-438.
3. Etingof, P., Golberg, O., Hensel, S., Liu, T., Schwendner, A., Vaintrob, D., Yudovina, E. (2011). Introduction to Representation Theory. American Mathematical Society.
4. Armstrong, M. A. (1979). Basic Topology. Undergraduate Texts in Mathematics.
5. Knapp, A. W. (1996). Lie Groups Beyond an Introduction. Progress in Mathematics,
6. Birkhäuser. Reid, M. (1988). Undergraduate Algebraic Geometry. Cambridge University Press.
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
- ISBN (Print)
- 978-1-83558-133-9
- ISBN (Online)
- 978-1-83558-134-6
- Published Date
- 17 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/11/20230382
- Copyright
- 17 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited