# Tensor product construction of 2-freeness

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 259-272
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topLenczewski, R.. "Tensor product construction of 2-freeness." Banach Center Publications 43.1 (1998): 259-272. <http://eudml.org/doc/208846>.

@article{Lenczewski1998,

abstract = {From a sequence of m-fold tensor product constructions that give a hierarchy of freeness indexed by natural numbers m we examine in detail the first non-trivial case corresponding to m=2 which we call 2-freeness. We show that in this case the constructed tensor product of states agrees with the conditionally free product for correlations of order ≤ 4. We also show how to associate with 2-freeness a cocommutative *-bialgebra.},

author = {Lenczewski, R.},

journal = {Banach Center Publications},

keywords = {2-freeness; tensor product of states; conditionally free product for correlations; free -algebras; double tensor product; infinite tensor product of -algebras; cocommutative -bialgebra},

language = {eng},

number = {1},

pages = {259-272},

title = {Tensor product construction of 2-freeness},

url = {http://eudml.org/doc/208846},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Lenczewski, R.

TI - Tensor product construction of 2-freeness

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 259

EP - 272

AB - From a sequence of m-fold tensor product constructions that give a hierarchy of freeness indexed by natural numbers m we examine in detail the first non-trivial case corresponding to m=2 which we call 2-freeness. We show that in this case the constructed tensor product of states agrees with the conditionally free product for correlations of order ≤ 4. We also show how to associate with 2-freeness a cocommutative *-bialgebra.

LA - eng

KW - 2-freeness; tensor product of states; conditionally free product for correlations; free -algebras; double tensor product; infinite tensor product of -algebras; cocommutative -bialgebra

UR - http://eudml.org/doc/208846

ER -

## References

top- [B-L-S] M. Bożejko, M. Leinert and R. Speicher, Convolution and limit theorems for conditionally free random variables, Pac. J. Math. 175, No.2 (1996), 357-388. Zbl0874.60010
- [Len1] R. Lenczewski, On sums of q-independent $S{U}_{q}\left(2\right)$ quantum variables, Comm. Math. Phys. 154 (1993), 127-134. Zbl0788.60016
- [Len2] R. Lenczewski, Addition of independent variables in quantum groups, Rev. Math. Phys. 6 (1994), 135-147. Zbl0793.60116
- [Sch] M. Schürmann, White Noise on Bialgebras, Springer-Verlag, Berlin, 1993. Zbl0773.60100
- [V-D-N] D. V. Voiculescu, K. J. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, AMS, Providence, 1992.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.