{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86940"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86940","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Double Crossproducts of Hopf* Algebras, Discrete Quantum Groups and Amenable Groups","abstract":"In Appendix A, we consider a third construction, the bicrossproduct which is a simultaneous cross product/cross coproduct construction. We find conditions which ensure that the bicrossproduct of two Hopf $\\sp{\\*}$ algebras is a Hopf $\\sp{\\*}$ algebra. In Appendix B, we provide physical motivation for studying bicrossproducts by describing a possible theory of quantum gravity where the algebra of quantum observables is a bicrossproduct.","abstract_html":"In Appendix A, we consider a third construction, the bicrossproduct which is a simultaneous cross product/cross coproduct construction. We find conditions which ensure that the bicrossproduct of two Hopf $\\sp{\\*}$ algebras is a Hopf $\\sp{\\*}$ algebra. 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We find conditions which ensure that the bicrossproduct of two Hopf $\\sp{\\*}$ algebras is a Hopf $\\sp{\\*}$ algebra. In Appendix B, we provide physical motivation for studying bicrossproducts by describing a possible theory of quantum gravity where the algebra of quantum observables is a bicrossproduct.","Made available in DSpace on 2015-09-28T15:20:16Z (GMT). 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We find conditions which ensure that the bicrossproduct of two Hopf $\\sp{\\*}$ algebras is a Hopf $\\sp{\\*}$ algebra. In Appendix B, we provide physical motivation for studying bicrossproducts by describing a possible theory of quantum gravity where the algebra of quantum observables is a bicrossproduct.","Made available in DSpace on 2015-09-28T15:20:16Z (GMT). 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