Geodesic
Isomorphy Classes of Involutions of SO(n, k, β), n>2
Robert W. Benim1 ; Christopher E. Dometrius2 ; Aloysius G. Helminck3 ; Ling Wu3
1Dept. of Mathematics and Computer Science, Pacific University, 2043 College Way, Forest Grove, OR 97116, U.S.A.
2Math, Science and Technologies Division, Forsyth Technical Community College, 100 Silas Creek Parkway, Winston-Salem, NC 27103, U.S.A.
3Dept. of Mathematics, North Carolina State University, 2108 SAS Hall, Box 8205, Raleigh, NC 27695, U.S.A.
Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 383-438

Voir la notice de l'article provenant de la source Heldermann Verlag

A first characterization of the isomorphism classes of k-involutions for any reductive algebraic group 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 by A. G. Helminck, L. Wu and C. Dometrius [Involutions of Sl(n, k), (n > 2), Acta Appl. Math. 90 (2006) 91--119] a full classification of all k-involutions on SL(n,k) for k algebraically closed, the real numbers, the p-adic numbers or a finite field was provided. In a paper by R. W. Benim, A. G. Helminck and F. Jackson Ward [Isomorphy classes of involutions of Sp(2n,k), n>2, J. of Lie Theory 25 (2015) 903--947] a similar classification was given for all k-involutions of SP(2n,k).
In this paper, we find analogous results to develop a detailed characterization of the k-involutions of SO(n,k,β), where β is any non-degenerate symmetric bilinear form and k is any field not of characteristic 2. We use these results to characterize the isomorphy classes of k-involutions of SO(n,k,β) for all bilinear forms, β when char(k) is not equal to 2 or 3, and for some bilinear forms when char(k) = 3. When n unequal 3, 4, 6, 8, then the characterization considers all involutions. If n = 3, 4, 6, 8, then the characterization only considers inner involutions.
Classification : 14M15, 20G05, 20G15, 20K30
Mots-clés : Orthogonal Group, symmetric spaces, involutions, inner automophisms

Robert W. Benim  1   ; Christopher E. Dometrius  2   ; Aloysius G. Helminck  3   ; Ling Wu  3

1 Dept. of Mathematics and Computer Science, Pacific University, 2043 College Way, Forest Grove, OR 97116, U.S.A.
2 Math, Science and Technologies Division, Forsyth Technical Community College, 100 Silas Creek Parkway, Winston-Salem, NC 27103, U.S.A.
3 Dept. of Mathematics, North Carolina State University, 2108 SAS Hall, Box 8205, Raleigh, NC 27695, U.S.A. 
Robert W. Benim; Christopher E. Dometrius; Aloysius G. Helminck; Ling Wu. Isomorphy Classes of Involutions of SO(n, k, β), n>2. Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 383-438. http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a3/
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     author = {Robert W. Benim and Christopher E. Dometrius and Aloysius G. Helminck and Ling Wu},
     title = {Isomorphy {Classes} of {Involutions} of {SO(n,} k, \ensuremath{\beta}), n>2},
     journal = {Journal of Lie Theory},
     pages = {383--438},
     year = {2016},
     volume = {26},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a3/}
}
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