More examples of invariance under twisting

Florin Panaite

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 1, page 187-195
  • ISSN: 0011-4642

Abstract

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The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are particular cases of invariance under twisting, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery duality theorem.

How to cite

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Panaite, Florin. "More examples of invariance under twisting." Czechoslovak Mathematical Journal 62.1 (2012): 187-195. <http://eudml.org/doc/246294>.

@article{Panaite2012,
abstract = {The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are particular cases of invariance under twisting, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery duality theorem.},
author = {Panaite, Florin},
journal = {Czechoslovak Mathematical Journal},
keywords = {twisted tensor product; invariance under twisting; duality theorem; twisted tensor products; invariance under twisting; duality theorems; smash products; Drinfeld twistings; Drinfeld doubles; quasitriangular Hopf algebras},
language = {eng},
number = {1},
pages = {187-195},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {More examples of invariance under twisting},
url = {http://eudml.org/doc/246294},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Panaite, Florin
TI - More examples of invariance under twisting
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 187
EP - 195
AB - The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are particular cases of invariance under twisting, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery duality theorem.
LA - eng
KW - twisted tensor product; invariance under twisting; duality theorem; twisted tensor products; invariance under twisting; duality theorems; smash products; Drinfeld twistings; Drinfeld doubles; quasitriangular Hopf algebras
UR - http://eudml.org/doc/246294
ER -

References

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  4. Fiore, G., 10.1088/0305-4470/35/3/312, J. Phys. A, Math. Gen. 35 (2002), 657-678. (2002) Zbl1041.81064MR1957140DOI10.1088/0305-4470/35/3/312
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  6. Guccione, J. A., Guccione, J. J., Semiquasitriangular Hopf algebras, Electronic preprint arXiv:math.QA/0302052. 
  7. Guccione, J. A., Guccione, J. J., 10.1016/S0021-8693(02)00546-X, J. Algebra 261 (2003), 54-101. (2003) Zbl1017.16032MR1967157DOI10.1016/S0021-8693(02)00546-X
  8. Martínez, P. Jara, Peña, J. López, Panaite, F., Oystaeyen, F. Van, 10.1142/S0129167X08004996, Int. J. Math. 19 (2008), 1053-1101. (2008) MR2458561DOI10.1142/S0129167X08004996
  9. Majid, S., 10.1080/00927879108824306, Commun. Algebra 19 (1991), 3061-3073. (1991) Zbl0767.16014MR1132774DOI10.1080/00927879108824306
  10. Năstăsescu, C., Panaite, F., Oystaeyen, F. Van, 10.1023/A:1009931309850, Algebr. Represent. Theory 2 (1999), 211-226. (1999) MR1715183DOI10.1023/A:1009931309850
  11. Daele, A. Van, Keer, S. Van, The Yang-Baxter and pentagon equation, Compos. Math. 91 (1994), 201-221. (1994) Zbl0811.17014MR1273649

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