Preview

Doklady of the National Academy of Sciences of Belarus

Advanced search

ON REDUCED WHITEHEAD GROUPS OF SPECIAL UNITARY GROUPS OF ANISOTROPIC HERMITIAN FORMS, RELATED TO HENSELIAN DIVISION ALGEBRAS WITH GLOBAL RESIDUE ALGEBRAS

Abstract

The aim of the given paper is to obtain a scheme of computation of reduced Whitehead groups of special unitary groups of anisotropic hermitian forms, related to henselian division algebras with global residue algebras.

About the Author

V. I. YANCHEVSKIĬ
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus


References

1. Segev, Y. On finite homomorphic images of the multiplicative groups of a division algebra / Y. Segev // Ann. Math. – 1999. – T. 149, N 1. – P. 219–251.

2. Chernousov, V. R-equivalence and special unitary groups / V. Chernousov, A. Merkurjev // J. Algebra. – 2002. – T. 209, N 1. – P. 175–198.

3. Draxl, P. SK1 von Algebren über vollständig diskret bewerteten Körpern und Galoiskohomologie abelscher Körpererweiterungen / P. Draxl // J. reine angew. Math. – 1977. – Bd. 293–294. – P. 116–142.

4. Hazrat, R. Unitary SK1 of graded and valued division algebras / R. Hazrat, A. R. Wadsworth // Proc. London Math. Soc. – 2011. – Vol. 103, N 3. – P. 508–534.

5. Wadsworth, A. R. Unitary SK1 for a graded division ring and its quotient division ring / A. R. Wadsworth, V. I. Yanchevskiĭ // J. Algebra. – 2012. – Vol. 352, N 1. – P. 62–78.

6. Yanchevskiĭ, V. I. Whitehead groups and groups of R-equivalence classes of linear algebraic groups of noncommutative classical type over some virtual fields / V. I. Yanchevskiĭ // Proceeding of the International Conference on Algebraic Groups and Arithmetic, TIFR, Mumbai, December 2001. – Mumbai, 2001. – P. 491–505.

7. Платонов, В. П. Проблема Таннака–Артина и приведенная К-теория / В. П. Платонов // Изв. АН СССР, сер. мат. – 1976. – T. 40, № 2. – С. 227–261.

8. Янчевский, В. И. Простые алгебры с инволюциями и унитарные группы / В. И. Янчевский // Матем. сб. – 1974. – T. 93, № 3. – С. 368–380.

9. Янчевский, В. И. Приведенная К-теория и тела над гензелевыми дискретно нормированными полями / В. И. Янчевский // Изв. АН СССР, сер. мат. – 1978. – T. 42, № 4. – С. 879–918.

10. Янчевский, В. И. Приведенная унитарная К-теория. Приложения к алгебраическим группам / В. И. Янчевский // Матем. сб. – 1979. – T. 110(152), № 4(12). – С. 579–596.

11. Kneser, M. Orthogonale Gruppen über algebraischen Zahlkörpern / M. Kneser // J. reine angew. Math. – 1956. – N 196. – Р. 213–220.

12. Sethuraman, B. A. On the special unitary group of a division algebra / B. A. Sethuraman, B. Sury // Proc. Amer. Math. Soc. – 2006. – Vol. 134, N 2. – P. 351–354.

13. Sury, B. On SU(1, D)/ [U(1,D), U(1,D)] for a quaternion division algebra D / B. Sury // Arch. Math. – 2008. – Vol. 90, N 6. – P. 493–500.

14. Yanchevskiĭ, V. I. Reduced Whitehead groups and the conjugacy problem for special unitary groups of anisotropic Hermitian forms / V. I. Yanchevskiĭ // J. Math. Sci. – 2013. – Vol. 192, N 2. – P. 250–262.


Review

Views: 789


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)