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On reduced anisotropic unitary Whitehead groups of henselian division algebras which are either unramified or tamely ramified with commutative residue algebras

https://doi.org/10.29235/1561-8323-2021-65-1-7-10

Abstract

Reduced anisotropic unitary Whitehead groups of henselian division algebras, which are either unramified or tamely ramified with commutative residue algebra, are computed.

About the Author

V. I. Yanchevskii
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus

Yanchevskii Vyacheslav I. – Academician, D. Sc. (Physics and Mathematics), Professor, Head of the Department

11, Surganov Str., 220072, Minsk



References

1. Sethuraman B. A., Sury B. A note on the special unitary group of a division algebra. Proceedings of the American Mathematical Society, 2005, vol. 134, no. 2, pp. 351–354. https://doi.org/10.1090/s0002-9939-05-07985-2

2. Sury B. On SU(1, D) / [U(1, D), U(1, D)] for a quaternion division algebra D. Archiv der Mathematik, 2008, vol. 90, no. 6, pp. 493–500. https://doi.org/10.1007/s00013-008-2438-x

3. Yanchevskii V. I. Reduced Whitehead groups and the conjugacy problem for special unitary groups of anisotropic Hermitian forms. Journal of Mathematical Sciences, 2013, vol. 192, no. 2, pp. 250–262. https://doi.org/10.1007/s10958-013-1391-9

4. Albert A. A. Involutorial simple algebras and real Riemann matrices. Annals of Mathematics, 1935, vol. 36, no. 4, pp. 886–964. https://doi.org/10.2307/1968595


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