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

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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},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {196--209},
     publisher = {mathdoc},
     volume = {388},
     year = {2011},
     language = {ru},
     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/