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ERGODIC ACTIONS OF CONVERGENT FUCHSIAN GROUPS ON QUOTIENTS OF THE NONCOMMUTATIVE HARDY
 

Summary: ERGODIC ACTIONS OF CONVERGENT FUCHSIAN GROUPS
ON QUOTIENTS OF THE NONCOMMUTATIVE HARDY
ALGEBRAS
ALVARO ARIAS AND FRŽEDŽERIC LATRŽEMOLI`ERE
Abstract. We establish that particular quotients of the non-commutative
Hardy algebras carry ergodic actions of convergent discrete subgroups of the
group SU(n, 1) of automorphisms of the unit ball in Cn. To do so, we provide
a mean to compute the spectra of quotients of noncommutative Hardy algebra
and characterize their automorphisms in term of biholomorphic maps of the
unit ball in Cn.
We establish that given any discrete subgroup of SU(n, 1) such that the orbit of
0 for the action of on the open unit ball Bn of Cn
satisfies the Blaschke condition:

(1 - (0) Cn ) < ,
there exists a quotient algebra of the noncommutative Hardy algebra F
n whose
group of weak* continuous automorphisms is the stabilizer of the orbit of 0 for
in Bn. Moreover, acts ergodically on this quotient algebra. Our methods rely
heavily on the theory of analytic functions in several variables.

  

Source: Arias, Alvaro - Department of Mathematics, University of Denver

 

Collections: Mathematics