Restricted Lie Algebras via Monadic Decomposition
- 31 Downloads
We give a description of the category of restricted Lie algebras over a field \(\Bbbk \) of prime characteristic by means of monadic decomposition of the functor that computes the \(\Bbbk \)-vector space of primitive elements of a \(\Bbbk \)-bialgebra.
KeywordsMonads Restricted Lie algebras
Mathematics Subject Classification (2010)Primary 18C15 Secondary 16S30
Unable to display preview. Download preview PDF.
This note was written while the first and the third authors were members of the ”National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA-INdAM). The first author was partially supported by the research grant “Progetti di Eccellenza 2011/2012” from the “Fondazione Cassa di Risparmio di Padova e Rovigo”. He thanks the members of the department of Mathematics of both Vrije Universiteit Brussel and Université Libre de Bruxelles for their warm hospitality and support during his stay in Brussels in August 2013, when the work on this paper was initiated. The second named author acknowledges the financial support of an INdAM Marie Curie Fellowship.
- 2.Appelgate, H., Tierney, M.: Categories with models. 1969 Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67). Springer, Berlin (1969)Google Scholar
- 10.Grünenfelder, L.: UBER DIE STRUKTUR VON HOPF-ALGEBREN. Dissertation ETH Zürich (1969)Google Scholar
- 15.Michaelis, W.: The Primitives of the Continuous Linear Dual of a Hopf Algebra as the Dual Lie Algebra of a Lie Coalgebra. Lie Algebra and Related Topics (Madison, WI, 1988), 125–176, Contemp Math., vol. 110. Amer. Math. Soc., Providence (1990)Google Scholar