A Note on the Inverse Limits of Linear Algebraic Groups
نویسندگان
چکیده
In this paper, we investigate some properties of inverse limits of linear algebraic groups. For example, we show that if G = lim ←−Gi, where (Gi, πji)i,j∈I is an inverse system of algebraic groups over an algebraically closed field. Then each canonical projection πi : G → Gi maps closed subgroups of G onto closed subgroups of Gi. Furthermore, we prove directly that the inverse limit of an inverse system of linear algebraic groups, which may fail to be compact, is always linearly compact. We introduce also two types of categories: ΣN and ΣC and we generalize our results to the new larger categories. Mathematics Subject Classification: 14L, 16W, 17B45
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