The Derivation Algebra of the Extended Conformal Galilei Algebra
We investigate the derivation algebra of the mass-extended conformal Galilei algebra over the
field of complex numbers. The algebra is realized as a one-dimensional central extension of the conformal
Galilei algebra. We determine the derivations and identify the distinguished outer derivation which acts by
one half on the translation module and by the identity on the central element. We then establish completeness
of the derivation algebra and describe the associated derivation tower.
1. Y. Su and L. Zhu, Derivation algebras of centerless perfect Lie algebras are complete, J. Algebra 290 (2005),
484–494.
2. S. Alauadinov and Sh. Yusupov, Local derivations of conformal Galilei algebra, Commun. Algebra 52 (2024),
2489–2508.
3. Y. Gao, Y. Liu and Y. Pei, Structure of the planar Galilean conformal algebra, Rep. Math. Phys. 78 (2016),
107–122.
4. D. B. Fuks, Cohomology of Infinite-Dimensional Lie Algebras, Springer, New York, 1986.
5. N. Jacobson, Lie Algebras, Dover Publications, New York, 1979.
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