Twisted Smash Products and L-R Smash Products for Biquasimodule Hopf Quasigroups

REFERENCES

• Albert , A. A. ( 1943 ). Quasigroups I . Trans. Amer. Math. Soc. 54 : 507 – 519 .
   Google Scholar
• Bieliavsky , P. , Bonneau , P. , Maeda , Y. ( 2005 ). Universal deformation formulae for three-dimensional solvable Lie groups. In: Quantum field theory and noncommutative geometry . Lecture Notes in Phys. 662 : 127 – 141 .
   Google Scholar
• Bonneau , P. , Gerstenhaber , M. , Giaquinto , A. , Sternheimer , D. ( 2004 ). Quantum groups and deformation quantization: explicit approaches and implicit aspects . J. Math. Phys. 45 : 3703 – 3741 .
   Web of Science ®Google Scholar
• Brzeziński , T. ( 2010 ). Hopf modules and the fundamental theorem for Hopf (co)quasigroups . Int. Electronic J. Alg. 8 : 114 – 128 .
   Google Scholar
• Brzeziński , T. , Jiao , Z. M. ( 2012 ). Actions of Hopf quasigroups . Comm. Algebra 40 : 681 – 696 .
   Web of Science ®Google Scholar
• Brzeziński , T. , Jiao , Z. M. ( 2012 ). R-smash products of Hopf quasigroups . Arab. J. Math. 1 : 39 – 46 .
   Google Scholar
• Doi , Y. , Takeuchi , M. ( 1994 ). Mutiplication alteration by two-cocycle the quantum view . Comm. Algebra 22 : 5715 – 5732 .
   Web of Science ®Google Scholar
• Fang , X. L. , Wang , S. H. ( 2011 ). Twisted smash product for Hopf quasigroups . J. Southeast Univ. 27 : 343 – 346 .
   Google Scholar
• Klim , J. , Majid , S. ( 2010 ). Hopf quasigroups and the algebraic 7-sphere . J. Algebra 323 : 3067 – 3110 .
   Web of Science ®Google Scholar
• Molnar , R. K. ( 1977 ). Semi-direct products of Hopf algebras . J. Algebra 47 : 29 – 51 .
   Web of Science ®Google Scholar
• Panaite , F. , Van Oystaeyen , F. ( 2007 ). L-R-smash product for (quasi)-Hopf algebras . J. Algebra 309 : 168 – 191 .
   Web of Science ®Google Scholar
• Pérez-Izquierdo , J. M. ( 2007 ). Algebras, hyperalgebras, nonassociative bialgebras and loops . Adv. Math. 208 : 834 – 876 .
   Web of Science ®Google Scholar
• López López , M. P. , Villanueva Nóvoa , E. ( 2013 ). The antipode and the (co)invariants of a finite Hopf (co)quasigroup . Appl. Categor. Struct. 21 : 237 – 247 .
   Web of Science ®Google Scholar
• Radford , D. E. ( 1993 ). Minimal quasitriangular Hopf algebras . J. Algebra 157 : 285 – 315 .
   Web of Science ®Google Scholar
• Wang , S. H. , Li , J. Q. ( 1998 ). On twisted smash products for bimodule algebras and the Drinfeld double . Comm. Algebra 26 : 2435 – 2444 .
   Web of Science ®Google Scholar
• Zhang , L. Y. ( 2006 ). L-R smash products for bimodule algebras . Progress in Natural Science 16 : 580 – 587 .
   Web of Science ®Google Scholar
• Communicated by M. Cohen.
   Google Scholar