Algebraic structures based on a classifying space of a compact Lie group
The main purpose of this paper is to investigate the algebraic explanation based on a classifying space of the compact Lie group \(U(1)\) which is canonically isomorphic to the circle group \(S^1\). After constructing self-maps using the suspension structure, the author defines a useful commutator of self-maps on the suspension of a classifying space of the compact Lie group. He constructs the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products. He shows that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. By using the Milnor-Moore theorem, he also investigates the concrete primitive elements as the images of the Hurewicz homomorphisms in the Pontrjagin algebra. The paper is well written and organized. The reviewer wonders why the author published the paper in this journal. It should be published in a journal related to topology.
classifying space of a compact Lie group
scientific article; zbMATH DE number 6306956
scientific article