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Algebraic K-theory of the varieties $ \mathrm{SL}_{2n} / \mathrm{Sp}_{2n}$, $ \mathrm{E}_6 / \mathrm{F}_4$ and their twisted forms


Author: Maria Yakerson
Translated by: the author
Original publication: Algebra i Analiz, tom 28 (2016), nomer 3.
Journal: St. Petersburg Math. J. 28 (2017), 421-431
MSC (2010): Primary 19E08; Secondary 14M17
DOI: https://doi.org/10.1090/spmj/1457
Published electronically: March 29, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathrm {SL}_{2n}$, $ \mathrm {Sp}_{2n}$, $ \mathrm {E}_6 = G^{sc}(\mathrm {E}_6)$, $ \mathrm {F}_4 = G(\mathrm {F}_4)$ be simply connected split algebraic groups over an arbitrary field $ F$. Algebraic K-theory of the affine homogeneous varieties $ \mathrm {SL}_{2n}/\mathrm {Sp}_{2n}$ and $ \mathrm {E}_6/\mathrm {F}_4$ is computed. Moreover, explicit elements that generate $ K_*(\mathrm {SL}_{2n}/\mathrm {Sp}_{2n})$ and $ K_*(\mathrm {E}_6/\mathrm {F}_4)$ as $ K_*(F)$-algebras are provided. Also, K-theory is computed for some twisted forms of these varieties.


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  • 1. A. S. Merkur'ev, Comparison of the equivariant and the standard $ K$-theory of algebraic varieties, Algebra i Analiz 9 (1997), no. 4, 175-214; English transl., St. Petersburg Math. J. 9 (1998), no. 4, 815-850. MR 1604004
  • 2. I. A. Panin, Splitting principle and $ K$-theory of simply connected semisimple algebraic groups, Algebra i Analiz 10 (1998), no. 1, 88-131; English transl., St. Petersburg Math. J. 10 (1999), no. 1, 69-101. MR 1618404
  • 3. A. Ananyevskiy, On the algebraic K-theory of some homogeneous varieties, Doc. Math. 17 (2012), 167-193. MR 2946822
  • 4. M. Levine, The algebraic K -theory of the classical groups and some twisted forms, Duke Math. J. 70 (1993), no. 2, 405-443. MR 1219818
  • 5. W. G. McKay and J. Patera, Tables of dimensions, indices, and branching rules for representations of simple Lie algebras, Lecture Notes Pure Appl. Math., vol. 69, M. Dekker, Inc., New York, 1981. MR 0604363
  • 6. A. S. Merkurjev, Equivariant K-theory, Handbook of $ K$-theory, Vols. 1-2, Springer, Berlin, 2005, pp. 925-954. MR 2181836
  • 7. H. Minami, K-groups of symmetric spaces. I, Osaka J. Math. 12 (1975), no. 3, 623-634. MR 0415646
  • 8. I. A. Panin, On the algebraic K-theory of twisted flag varieties, K-Theory 8 (1994), no. 6, 541-585. MR 1326751
  • 9. D. Quillen, Higher algebraic K-theory. I, Lecture Notes in Math., vol. 341, Springer, Berlin, 1972, pp. 85-147. MR 0338129
  • 10. R. W. Richardson, Affine coset spaces of reductive algebraic groups, Bull. London Math. Soc. 9 (1977), no. 1, 38-41. MR 0437549
  • 11. R. Steinberg, On a theorem of Pittie, Topology 14 (1975), 173-177. MR 0372897
  • 12. R. Swan, K-theory of quadric hypersurfaces, Ann. of Math. (2) 121 (1985), no. 1, 113-153. MR 799254
  • 13. J. Tits, Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque, J. Reine Angew. Math. 247 (1971), 196-220. MR0277536

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Additional Information

Maria Yakerson
Affiliation: Department of Mathematics, University of Duisburg-Essen Thea-Leymann-Str. 9 45127, Essen, Germany
Email: mura.yakerson@gmail.com

DOI: https://doi.org/10.1090/spmj/1457
Keywords: Algebraic K-theory, affine homogeneous varieties
Received by editor(s): October 24, 2015
Published electronically: March 29, 2017
Additional Notes: Supported by the grant Sonderforschungsbereich Transregio 45
Dedicated: To Sasha Ivanov
Article copyright: © Copyright 2017 American Mathematical Society

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