Bull. Austral. Math. Soc. 72(1) pp.109--127, 2005.
Finite presentability of some metabelian Hopf algebras
Dessislava H. Kochloukova |
Partially supported by ``bolsa de produtividade de pesquisa" from CNPq, Brazil.
Abstract
We classify the Hopf algebras
U(L)#kQ of homological type
FP2 where L is a Lie algebra and Q an Abelian group such that L has an Abelian ideal A invariant under the Q-action via conjugation and U(L/A)#kQ is commutative.
This generalises the classification of finitely presented
metabelian Lie algebras given by J. Groves and R. Bryant.
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| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2162297 | Z'blatt-MATH: 02212189 |
References
- G. Baumslag;
Some remarks on finitely presented algebras,
J. Pure Appl. Algebra 8 (1976), pp. 187--196. MR437608 - M. Bestvina and N. Brady;
Morse theory and finiteness properties of groups,
Invent. Math. 129 (1997), pp. 445--470. MR1465330 - R. Bieri and J.R.J. Groves;
Metabelian groups of type FP∞ are virtually of type FP,
Proc. London Math. Soc. (3) 45 (1982), pp. 365--384. MR670042 - R. Bieri and R. Strebel;
Valuations and finitely presented metabelian groups,
Proc. London Math. Soc. (3) 41 (1980), pp. 439--464. MR591649 - R. Bryant and J.R.J. Groves;
Finite presentation of abelian-by-finite dimensional Lie algebras,
J. London Math. Soc. (2) 60 (1999), pp. 45--57. MR1721814 - R. Bryant and J.R.J. Groves;
Finitely presented Lie algebras,
J. Algebra 218 (1999), pp. 1--25. MR1704674 - D.H. Kochloukova;
Finite presentability and the homological type FPm for a class of Hopf algebras,
Comm. Algebra (to appear). - S. Montgomery;
Hopf algebras and their actions on rings,
CBMS Regional Conference Series in Mathematics 82 (American Mathematical Society, Providence, R.I., 1993). MR1243637
ISSN 0004-9727