MASUDA Tetsuya University of Tsukuba, Inst.of Math., 数学系, 助教授 (70202314)
MORITA Jun University of Tsukuba, Inst.of Math., 数学系, 教授 (20166416)
TAKEUCHI Mitsuhiro University of Tsukuba, Inst.of Math., 数学系, 教授 (00015950)
TANABE Kenichiro University of Tsukuba, Inst.of Math., 数学系, 助手 (10334038)
FUJITA Hisamasa University of Tsukuba, Inst.of Math., 数学系, 講師 (60143161)
|Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
Our new results are divided roughly into two. First, we have classified some range of coquasi-bialgebras, which generalize Hopf algebras, up to tensor equivalences of their comodule categories ; this was done by constructing related cohomology groups, in a very concrete way with use of braid diagrams. Second, we have obtained a new result on crossed products, and thereby proved in a unified way three famous theorems for affine group schemes ; this was based on the idea that the Hopf cohomology, which is non-abelian and multiplicative, can be approximated, in some sense, by the HochschiId cohomology, which is abelian and additive.
The results were annonced at the following conferences.
The 46-th Symposium on Algebra, Osaka Univ., July 30-August 2, 2001.
Non-commutative Geometry and Quantum Groups, Banach Center (Warsaw), September 17-29, 2001.