Finite Presentability And The Homological Type Fp M For A Class Of Hopf Algebras

We define and study the property finite presentability in the category ?? of Hopf algebras that are smash product of universal enveloping algebra of a Lie algebra by a group algebra. We show that for such Hopf algebras finite presentability is equivalent with finite presentability as an associative k -algebra.343785796Baumslag, G., Some remarks on finitely presented algebras (1976) J. Pure Appl. Algebra, 8, pp. 187-196Bieri, R., (1981) Homological Dimension of Discrete Groups. 2nd Ed., , London: Queen Mary College Mathematics NotesBrown, K.S., (1994) Cohomology of Groups, , Graduate Texts in Mathematics, 87. Springer-VerlagBryant, R., Groves, J.R.J., Finite presentation of Abelian-by-finite dimensional Lie algebras (1999) J. London Math. Soc. (2), 60 (1), pp. 45-57Bryant, R., Groves, J.R.J., Finitely presented Lie algebras (1999) J. Algebra, 218 (1), pp. 1-25Cartan, H., Eilenberg, S., (1956) Homological Algebra, , Princeton University PressChilds, L.N., (2000) Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, 80. , Math Surveys and Monographs, Providence, RI: Amer. Math. SocCohn, P.M., (1965) Universal Algebra, , Harper and RowKochloukova, D.H., Finite presentability of some metabelian Hopf algebras (2005) Bulletin Australian Math. Soc., 72 (1), pp. 109-127Montgomery, S., (1993) Hopf Algebras and Their Actions on Rings, , CBMS, Regional Conference Series in Mathematics 82Rotman, J., (1979) An Introduction to Homological Algebra, , New York: Academic pressWeibel, C.A., (1994) An Introduction to Homological Algebra, , Cambridge Studies in Advanced Mathematics 38. Cambridge University Pres