Geodesic
Another presentation of orthogonal Steinberg groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 46-59 Cet article a éte moissonné depuis la source Math-Net.Ru

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We use the pro-group approach to show that $\mathrm{StO}(M, q)$ admits van der Kallen’s “another presentation”, where $M$ is a module over a commutative ring with sufficiently isotropic quadratic form $q$. Moreover, we construct an analog of ESD-transvections in orthogonal Steinberg pro-groups under some assumptions on their parameters. 
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     author = {E. Yu. Voronetsky},
     title = {Another presentation of orthogonal {Steinberg} groups},
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E. Yu. Voronetsky. Another presentation of orthogonal Steinberg groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 46-59. http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a2/

[1] E. Yu. Voronetskii, Mladshaya $\mathrm{K}$-teoriya nechetnykh unitarnykh grupp, kandidatskaya dissertatsiya, SPbGU, Sankt-Peterburg, Rossiya, 2022

[2] V. A. Petrov, “Nechetnye unitarnye gruppy”, Zap. nauchn. semin. POMI, 305, 2003, 195–225

[3] M. S. Tulenbaev, “Multiplikator Shura gruppy elementarnykh matrits konechnogo poryadka”, Zap. nauchn. semin. LOMI, 86 (1979), 162–169 | MR | Zbl

[4] S. Böge, “Steinberggruppen von orthogonalen Gruppen”, J. reine angew. Math., 494 (1998), 219–236 | DOI | MR | Zbl

[5] A. Lavrenov, “Another presentation for symplectic Steinberg groups”, J. Pure Appl. Alg., 219:9 (2015), 3755–3780 | DOI | MR | Zbl

[6] A. Lavrenov, S. Sinchuk, “On centrality of even orthogonal $\mathrm{K}_2$”, J. Pure Appl. Alg., 221:5 (2017), 1134–1145 | DOI | MR | Zbl

[7] A. Lavrenov, S. Sinchuk, E. Voronetsky, Centrality of $\mathrm{K}_2$ for Chevalley groups: a pro-group approach, 2020, arXiv: 2009.03999

[8] B. A. Magurn, W. van der Kallen, L. N. Vaserstein, “Absolute stable rank and Witt cancellation for noncommutative rings”, Invent. Math., 91 (1988), 525–542 | DOI | MR | Zbl

[9] S. Sinchuk, “On centrality of $\mathrm{K}_2$ for Chevalley groups of type $\mathrm{E}_l$”, J. Pure Appl. Alg., 220:2 (2016), 857–875 | DOI | MR | Zbl

[10] W. van der Kallen, “Another presentation for Steinberg groups”, Indag. Math., 80:4 (1977), 304–312 | DOI | MR | Zbl

[11] E. Voronetsky, “Centrality of $\mathrm{K}_2$-functor revisited”, J. Pure Appl. Alg., 225:4 (1065) | DOI | MR

[12] E. Voronetsky, Centrality of odd unitary $\mathrm{K}_2$-functor, 2020, arXiv: 2005.02926 | MR

[13] E. Voronetsky, “Injective stability for odd unitary $\mathrm{K}_1$”, J. Group Theory, 23:5 (2020) | DOI | MR | Zbl

[14] M. Wendt, “On homotopy invariance for homology of rank two groups”, J. Pure Appl. Alg., 216:10 (2012), 2291–2301 | DOI | MR | Zbl