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- W4385963838 abstract "Isotropic odd unitary groups generalize the Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system $mathsf{BC}_ell$ and may be constructed by so-called odd form rings with Peirce decompositions. We show the converse: if a group $G$ has root subgroups indexed by roots of $mathsf{BC}_ell$ and satisfying natural conditions, then there is a homomorphism $mathrm{StU}(R, Delta) to G$ inducing isomorphisms on the root subgroups, where $mathrm{StU}(R, Delta)$ is the odd unitary Steinberg group constructed by an odd form ring $(R, Delta)$ with a Peirce decomposition. For groups with root subgroups indexed by $mathsf A_ell$ (the already known case) the resulting odd form ring is essentially a generalized matrix ring." @default.
- W4385963838 created "2023-08-18" @default.
- W4385963838 creator A5011504945 @default.
- W4385963838 date "2023-08-02" @default.
- W4385963838 modified "2023-09-26" @default.
- W4385963838 title "Groups with $mathsf{BC}_ell$-commutator relations" @default.
- W4385963838 doi "https://doi.org/10.48550/arxiv.2308.01225" @default.
- W4385963838 hasPublicationYear "2023" @default.
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