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Cohomology of Hopf algebras and Massey productsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Buchstaber Victor Matveevich, Popelenskii Fedor Yur'evich
- Журнал: Russian Mathematical Surveys
- Том: 79
- Номер: 4
- Год издания: 2024
- Издательство: Turpion - Moscow Ltd.
- Местоположение издательства: United Kingdom
- Первая страница: 567
- Последняя страница: 648
- DOI: 10.4213/rm10172e
- Аннотация: The theory of the trigraded Buchstaber spectral sequence Bss for graded Hopf algebras is developed. It is shown that the differentials of Bss define an increasing exhaustive filtration as a new structure in the cohomology of Hopf algebras. This structure is described explicitly for a number of known Hopf algebras. For the tensor algebra T(sExt^{1,∗}_A(k,k)) of the suspension of the one-dimensional cohomology of a Hopf algebra A over a field k, the construction of partial multivalued operations Bss_p, p⩾1, is presented. This construction is used to describe the differentials in the spectral sequence Bss and the exhaustive filtration in Ext^{∗,∗}_A(k,k). It is shown that the structure introduced is an effective tool for solving several well-known problems: (1) realising cohomology classes of Hopf algebras by Massey products; (2) interpreting differentials in Bss as Massey operations; (3) effective construction of a certain class of Massey products in the form of differentials in Bss.
- Добавил в систему: Бухштабер Виктор Матвеевич