Sofic Groups and Diophantine Approximation
نویسنده
چکیده
We prove the algebraic eigenvalue conjecture of J.Dodziuk, P.Linnell, V.Mathai, T.Schick and S.Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known, which is not sofic.
منابع مشابه
REFERENCES TO THE COURSE ”FINITE-DIMENSIONAL APPROXIMATION PROPERTIES OF FINITE GROUPS” References
[4] Lev Glebsky and Luis Manuel Rivera, Sofic groups and profinite topology on free groups, J. Algebra 320 (2008), no. 9, 3512-3518. [2] Misha Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109-197. [3] Gábor Elek and Endre Szabó, Hyperlinearity, essentially free actions and Linvariants. The sofic property, Math. Ann. 332 (2005), no. 2, 421-441...
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تاریخ انتشار 2007