Journal of Lie Theory

no. 1
Hodge Operators and Exceptional Isomorphisms between Unitary Groups
Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 329-360
We give a generalization of the Hodge operator to spaces (V,h) endowed with a hermitian or symmetric bilinear form h over arbitrary fields, including the characteristic two case. Suitable exterior powers of V become free modules over an algebra K defined using such an operator. This leads to several exceptional homomorphisms from unitary groups (with respect to h) into groups of semi-similitudes with respect to a suitable form over some subfield of K. The algebra K depends on h; it is a composition algebra unless h is symmetric and the characteristic is two.
DOI: 10.5802/jolt.1286
Classification: 20G15, 20E32, 20G20, 20G40, 22C05, 11E39, 11E57
Keywords: Hermitian form, symmetric bilinear form, exterior product, Pfaffian form, Hodge operator, exceptional isomorphism, composition algebra, quaternion algebra 
@article{JOLT_2023_33_1_a14,
     author = {L. Kramer and M. J. Stroppel},
     title = {Hodge {Operators} and {Exceptional} {Isomorphisms} between {Unitary} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {329--360},
     year = {2023},
     volume = {33},
     number = {1},
     doi = {10.5802/jolt.1286},
     zbl = {1522.20193},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1286/}
}
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L. Kramer; M. J. Stroppel. Hodge Operators and Exceptional Isomorphisms between Unitary Groups. Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 329-360. doi: 10.5802/jolt.1286

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