TY  - BOOK
AU  - Ershov,Mikhail
AU  - Jaikin-Zapirain,Andrei
AU  - Kassabov,Martin
TI  - Property (T) for groups graded by root systems
T2  - Memoirs of the American Mathematical Society
SN  - 9781470426040 (alk. paper)
U1  - 510 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society, 
KW  - Root systems (Algebra)
N1  - Includes bibliographical references and index; Chapter 1. Introduction --
Chapter 2. Preliminaries --
Chapter 3. Generalized spectral criterion --
Chapter 4. Root Systems --
Chapter 5. Property $(T)$ for groups graded by root systems --
Chapter 6. Reductions of root systems --
Chapter 7. Steinberg groups over commutative rings --
Chapter 8. Twisted Steinberg groups --
Chapter 9. Application: Mother group with property $(T)$ --
Chapter 10. Estimating relative Kazhdan constants --
Appendix A. Relative property $(T)$ for $(\mathrm St_n(R)\ltimes R^n,R^n)$
N2  - Introduces and studies the class of groups graded by root systems. The authors prove that if $\Phi$ is an irreducible classical root system of rank $\geq 2$ and $G$ is a group graded by $\Phi$, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of $G$.
ER  -