Hopf algebra actions and transfer of Frobenius and symmetric properties
DOI:
https://doi.org/10.7146/math.scand.a-115970Abstract
If $H$ is a finite-dimensional Hopf algebra acting on a finite-dimensional algebra $A$, we investigate the transfer of the Frobenius and symmetric properties through the algebra extensions $A^H\subset A\subset A\mathbin{\#} H$.
References
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Lam, T. Y., Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999. https://doi.org/10.1007/978-1-4612-0525-8
Montgomery, S., Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, vol. 82, American Mathematical Society, Providence, RI, 1993. https://doi.org/10.1090/cbms/082
Bergen, J., Constants of Lie algebra actions, J. Algebra 114 (1988), no. 2, 452–465. https://doi.org/10.1016/0021-8693(88)90303-1
Bergen, J., A note on smash products over Frobenius algebras, Comm. Algebra 21 (1993), no. 11, 4021–4024. https://doi.org/10.1080/00927879308824780
Brzezinski, T. and Wisbauer, R., Corings and comodules, London Mathematical Society Lecture Note Series, vol. 309, Cambridge University Press, Cambridge, 2003. https://doi.org/10.1017/CBO9780511546495
Caenepeel, S., Militaru, G., and Zhu, S., Frobenius and separable functors for generalized module categories and nonlinear equations, Lecture Notes in Mathematics, vol. 1787, Springer-Verlag, Berlin, 2002. https://doi.org/10.1007/b83849
Dăscălescu, S., Iovanov, M. C., and Preduţ, S., Frobenius structural matrix algebras, Linear Algebra Appl. 439 (2013), no. 10, 3166–3172. https://doi.org/10.1016/j.laa.2013.09.007
Dăscălescu, S., Năstăsescu, C., and Năstăsescu, L., Frobenius algebras of corepresentations and group-graded vector spaces, J. Algebra 406 (2014), 226–250. https://doi.org/10.1016/j.jalgebra.2014.02.020
Dăscălescu, S., Năstăsescu, C., and Năstăsescu, L., Graded semisimple algebras are symmetric, J. Algebra 491 (2017), 207–218. https://doi.org/10.1016/j.jalgebra.2017.08.009
Kadison, L., New examples of Frobenius extensions, University Lecture Series, vol. 14, American Mathematical Society, Providence, RI, 1999. https://doi.org/10.1090/ulect/014
Lam, T. Y., Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999. https://doi.org/10.1007/978-1-4612-0525-8
Montgomery, S., Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, vol. 82, American Mathematical Society, Providence, RI, 1993. https://doi.org/10.1090/cbms/082
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Published
2020-03-29
How to Cite
Dăscălescu, S., Năstăsescu, C., & Năstăsescu, L. (2020). Hopf algebra actions and transfer of Frobenius and symmetric properties. MATHEMATICA SCANDINAVICA, 126(1), 32–40. https://doi.org/10.7146/math.scand.a-115970
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