A natural ring basis for the shuffle algebra and an application to group schemes. (English) Zbl 0409.16011
MSC:
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 14L15 | Group schemes |
Keywords:
Free Semigroup on a Totally Ordered Set; Ring Basis; Shuffle Algebra; Commutative Pointed Irreducible Hopf Algebras; Primitive Elements; Augmentation Ideal; Factorization Theory; Prime Factorizations; Truncated Variable; Coradical Filtration; Solvable Affine Group SchemesReferences:
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| [2] | K. Newman and D. E. RadfordAmer. J. Math.; K. Newman and D. E. RadfordAmer. J. Math. · Zbl 0422.16003 |
| [3] | Radford, D. E., Commutative nearly primitively generated Hopf algebras, Comm. Algebra, 4, 9, 823-872 (1976) · Zbl 0346.16009 |
| [4] | Radford, D. E., On the structure of commutative pointed Hopf algebras, J. Algebra, 50, 284-296 (1978) · Zbl 0375.16009 |
| [5] | Sullivan, J. B., A decomposition theorem for pro-affine solvable groups over algebraically closed fields, Amer. J. Math., 95, 221-228 (1975) · Zbl 0272.14014 |
| [6] | Sweedler, M. E., Connected fully reducible affine group schemes in positive characteristic are abelian, J. Math. Kyoto Univ., 11, 51-70 (1971) · Zbl 0213.47204 |
| [7] | Sweedler, M. E., Hopf Algebras (1969), Benjamin: Benjamin New York · Zbl 0194.32901 |
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