Wyniki wyszukiwania

1

Quantum lens spaces and principal actions on graph C*-algebras

100%

Szymański W.

Banach Center Publications

|

2003

|

tom 61

|

nr 1

299-304

EN

We study certain principal actions on noncommutative C*-algebras. Our main examples are the $ℤ_p$- and 𝕋-actions on the odd-dimensional quantum spheres, yielding as fixed-point algebras quantum lens spaces and quantum complex projective spaces, respectively. The key tool in our analysis is the relation of the ambient C*-algebras with the Cuntz-Krieger algebras of directed graphs. A general result about the principality of the gauge action on graph algebras is given.

2

Quasi-diffusion solution of a stochastic differential equation

63%

Plucińska A., Szymański W.

Applicationes Mathematicae

|

2007

|

tom 34

|

nr 2

205-213

EN

We consider the stochastic differential equation $X_t = X₀ + ∫_0^t (A_s + B_s X_s)ds + ∫_0^t C_s dY_s$, where $A_t$, $B_t$, $C_t$ are nonrandom continuous functions of t, X₀ is an initial random variable, $Y = (Y_t, t ≥ 0)$ is a Gaussian process and X₀, Y are independent. We give the form of the solution ($X_t$) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ($X_t$) is a quasi-diffusion proces.

3

Endomorphisms of the Cuntz algebras

51%

Conti R., Hong J., Szymański W.

Banach Center Publications

|

2011

|

tom 96

|

nr 1

81-97

EN

This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor set. An identification of the image in Out(𝓞ₙ) of the restricted Weyl group with the group of automorphisms of the full two-sided n-shift is given, for prime n, providing an answer to a question raised by Cuntz in 1980. Furthermore, we discuss proper endomorphisms of 𝓞ₙ which preserve either the canonical UHF-subalgebra or the diagonal MASA, and present methods for constructing exotic examples of such endomorphisms.

Ograniczanie wyników

2 Banach Center Publications

1 Applicationes Mathematicae

3 Szymański W.

1 Conti R.

1 Hong J.

1 Plucińska A.

1 2011

1 2007

1 2003

Quantum lens spaces and principal actions on graph C*-algebras

Quasi-diffusion solution of a stochastic differential equation

Endomorphisms of the Cuntz algebras