Structure of Hyperbolic Unitary Groups I: Elementary Subgroups
By A. Bak, Nikolai Vavilov. 2000
110 citations recorded by the source corpus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/94496da5817e7dc03fd672c4a65d647af373b12f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
- Nikolai Vavilov
- Roozbeh Hazrat
- V. Petrov
- Sergey I. Nikolenko
- Misha Gavrilovich
- Alexei Stepanov
- A. Bak
- A. Stavrova
In Geometry and Topology
- Nikolai Vavilov
- Roozbeh Hazrat
- V. Petrov
- Sergey I. Nikolenko
- Misha Gavrilovich
- Alexei Stepanov
- A. Bak
- A. Stavrova
In Mathematical Physics
Citations in the corpus
- Dimension theory and nonstable K1 of quadratic modules (2002, methodology): “In the quadratic situation, the normality of the elementary subgroup is proved in Bak-Vavilov [4] by generalizing methods used in [3] and again in Bak-Vavilov [5] by developing a quadratic analog of the transvection procedure used in Stepanov-Vavilov [12].”
- K1 of Chevalley groups are nilpotent (2003, methodology): “There are numerous generalisations and ramifications of these methods for noncommutative rings, including the very powerful Golubchik-Mikhalev non-commutative localisation methods, see references in [25], [5], [16], which we do not discuss here, since we are only interested in commutative rings.”
- Odd Unitary Groups (2005, background): “The quadratic group GQ(V, q) is the group of all bijective isometriess of the form q, that is, the group consisting of all g ∈ GL(V ) such that B(gu, gv )= B(u, v )a ndQ(gu )= Q(u) for every u, v ∈ V .I n the case whereV is a hyperbolic space of rank l (then GQ(V, q )i s denoted by GQ 2l (R, Λ)) one”
- Structure of Chevalley groups: The proof from the book (2007, background): “In [66, 34 , 57], one can find a thorough survey of that stage of the theory and many dozens of further references.”
- Overgroups of Unitary Groups (2003, methodology): “(They formulate it in the terms of asr, but they use only the property of stability of KU1 in rings obtained by localization.) See also [ 5, Theorem 1.1 ] and [7, Theorem 4.4] for the case of almost commutative rings and central ¯ 1.”