Property (T) for noncommutative universal lattices
By Mikhail Ershov, A. Jaikin‐Zapirain. 2008
94 citations recorded by the source corpus.
We establish a new spectral criterion for Kazhdan’s property (T) which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property (T) for the groups ELn(R), where n≥3 and R is an arbitrary finitely generated associative ring. We also strengthen some of the results on property (T) for Kac-Moody groups from (Dymara and Januszkiewicz in Invent. Math. 150(3):579–627, 2002).
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/727830cb3d68f9c3f98f9253c51b2b558550b8bb
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Speed of random walks, isoperimetry and compression of finitely generated groups (2015, unknown): “1142/97898143243590069 [38] Ershov, Mikhail; Jaikin-Zapirain, Andrei, Property ({T}) for noncommutative universal lattices, Invent.”
- Expander graphs in pure and applied mathematics (2011, background): “n(R). The groups E n(R) play an important role in algebraic K-theory. If Ris a nitely generated ring then E n(R) is a nitely generated group (for n3). We can now state: 16 Theorem 2.6 (Ershov-Jaikin [EJ]). Let R be the free ring R = Zhx 1;:::;x riin the non-commutative free variables x 1;:::;x r. Th”
- Normal subgroups in the Cremona group (2010, unknown): “By the Shalom-Vaserstein Theorem (see [27]), ELd(A) has Kazhdan’s Property (T) and in particular has a fixed point in T , so F has a fixed point in T .”