Tensor product construction of 2-freeness

R. Lenczewski

Banach Center Publications (1998)

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

Abstract

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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.

How to cite

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Lenczewski, 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

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  1. [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
  2. [Len1] R. Lenczewski, On sums of q-independent S U q ( 2 ) quantum variables, Comm. Math. Phys. 154 (1993), 127-134. Zbl0788.60016
  3. [Len2] R. Lenczewski, Addition of independent variables in quantum groups, Rev. Math. Phys. 6 (1994), 135-147. Zbl0793.60116
  4. [Sch] M. Schürmann, White Noise on Bialgebras, Springer-Verlag, Berlin, 1993. Zbl0773.60100
  5. [V-D-N] D. V. Voiculescu, K. J. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, AMS, Providence, 1992. 

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