Geodesic
Invariant subalgebras of involutorial quaternion division algebras
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 21, Tome 388 (2011), pp. 196-209 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $K/k$ be a separable quadratic field extension. For quaternion division algebras with $K/k$ involutions $\tau$ their $\tau$-invariant $k$-subalgebras are studied. We give a complete description of such subalgebras up to $k$-isomorphisms. 
@article{ZNSL_2011_388_a8,
     author = {A. V. Prokopchuk and V. I. Yanchevskiǐ},
     title = {Invariant subalgebras of involutorial quaternion division algebras},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a8/}
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A. V. Prokopchuk; V. I. Yanchevskiǐ. Invariant subalgebras of involutorial quaternion division algebras. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 21, Tome 388 (2011), pp. 196-209. http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a8/

[1] A. A. Albert, Structure of Algebras, AMS, N.-Y., 1980

[2] Zh. Dëdonne, Geometriya klassicheskikh grupp, Mir, M., 1974 | MR

[3] N. Burbaki, Algebra. Moduli, koltsa, formy, Nauka, M., 1966 | MR

[4] B. A. Sethuraman, B. Sury, “On the special unitary group of a division algebra”, Proc. Amer. Math. Soc., 134 (2005), 351–354 | DOI | MR

[5] V. I. Yanchevskii, “Ob abelevykh faktorakh spetsialnykh unitarnykh grupp anizotropnykh form”, Dokl. NAN Belarusi, 2011, (prinyata k pechati)

[6] B. Sury, “On $\mathrm{SU}(1,D)/[U(1,D),U(1,D)]$ for a quaternion division algebra $D$”, Arch. Math., 90 (2008), 493–500 | DOI | MR | Zbl