Journal of Lie Theory

no. 4
Isomorphy Classes of Involutions of SP(2n, k), n>2
Journal of Lie Theory, Volume 25 (2015) no. 4, pp. 903-947
A first characterization of the isomorphism classes of k-involutions for any reductive algebraic groups defined over a perfect field was given by A. G. Helminck [On the Classification of k-involutions I, Adv. in Math. 153 (2000) 1--117] using 3 invariants. In another paper of A. G. Helminck, Ling Wu and C. Dometrius [Involutions of Sl(n, k), (n > 2), Acta Appl. Math. 90 (2006) 91--119] a classification of all involutions on SL(n,k) for k algebraically closed, the real numbers, the p-adic numbers or a finite field was provided. In this paper, we build on these results to develop a detailed characterization of the involutions of SP(2n,k). We use these results to classify the isomorphy classes of involutions of SP(2n, k) where k is any field not of characteristic 2.
DOI: 10.5802/jolt.866
Classification: 20G15, 20K30
Keywords: Symplectic Group, Involutions, Inner-automophisms 
@article{JOLT_2015_25_4_a0,
     author = {R. W. Benim and A. G. Helminck and F. Jackson Ward},
     title = {Isomorphy {Classes} of {Involutions} of {SP(2n,} k), n>2},
     journal = {Journal of Lie Theory},
     pages = {903--947},
     year = {2015},
     volume = {25},
     number = {4},
     doi = {10.5802/jolt.866},
     zbl = {1342.20047},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.866/}
}
TY  - JOUR
AU  - R. W. Benim
AU  - A. G. Helminck
AU  - F. Jackson Ward
TI  - Isomorphy Classes of Involutions of SP(2n, k), n>2
JO  - Journal of Lie Theory
PY  - 2015
SP  - 903
EP  - 947
VL  - 25
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.866/
DO  - 10.5802/jolt.866
ID  - JOLT_2015_25_4_a0
ER  - 
%0 Journal Article
%A R. W. Benim
%A A. G. Helminck
%A F. Jackson Ward
%T Isomorphy Classes of Involutions of SP(2n, k), n>2
%J Journal of Lie Theory
%D 2015
%P 903-947
%V 25
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.866/
%R 10.5802/jolt.866
%F JOLT_2015_25_4_a0
R. W. Benim; A. G. Helminck; F. Jackson Ward. Isomorphy Classes of Involutions of SP(2n, k), n>2. Journal of Lie Theory, Volume 25 (2015) no. 4, pp. 903-947. doi: 10.5802/jolt.866

Cited by Sources: