Analytic left algebraic groups. II

Magid, Andy R.

doi:10.1090/S0002-9947-1978-0473033-X

Analytic left algebraic groups. II
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by Andy R. Magid

Trans. Amer. Math. Soc. 238 (1978), 165-177

DOI: https://doi.org/10.1090/S0002-9947-1978-0473033-X

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Abstract:

An analytic left algebraic group is a complex analytic group carrying a structure of affine algebraic variety such that left translations by fixed elements are morphisms. The core of such a group is the (algebraic) subgroup of all elements such that right translation by them is a morphism. It is shown that the core determines the left algebraic structure, and this is used to determine when left algebraic structures are conjugate by inner automorphisms.

References

Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042

La torsion homologique et les sections rationnelles

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G. Hochschild and G. D. Mostow, On the algebra of representative functions of an analytic group, Amer. J. Math. 83 (1961), 111–136. MR 141732, DOI 10.2307/2372724
James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842, DOI 10.1007/978-1-4612-6398-2
Andy R. Magid, Left algebraic groups, J. Algebra 35 (1975), 253–272. MR 437548, DOI 10.1016/0021-8693(75)90050-2
Andy R. Magid, Analytic left algebraic groups, Amer. J. Math. 99 (1977), no. 5, 1045–1059. MR 447262, DOI 10.2307/2373999
Maxwell Rosenlicht, On quotient varieties and the affine embedding of certain homogeneous spaces, Trans. Amer. Math. Soc. 101 (1961), 211–223. MR 130878, DOI 10.1090/S0002-9947-1961-0130878-0