Hasse–Schmidt derivations, divided powers and differential smoothness

Luis Narváez Macarro

Displaying similar documents to “Hasse–Schmidt derivations, divided powers and differential smoothness”

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

Similarity:

We construct a subalgebra $Σ^{'} (W_{n})$ of dimension $2 \cdot 3^{n - 1}$ of the group algebra of the Weyl group $W_{n}$ of type $B_{n}$ containing its usual Solomon algebra and the one of $𝔖_{n}$ : $Σ^{'} (W_{n})$ is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras $Σ^{'} (W_{n}) \to Z Irr (W_{n})$ . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to $W_{n}$ . In an appendix, P. Baumann and C. Hohlweg present in an...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

Similarity:

Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...

On some formula in connected cocommutative Hopf algebras over a field of characteristic 0

Piotr Wiśniewski (2000)

Colloquium Mathematicae

Similarity:

Let H be a cocommutative connected Hopf algebra, where K is a field of characteristic zero. Let $H^{+} = K e r$ and $h^{+} = h - (h)$ for $h \in H$ . We prove that $d_{h} = \sum_{r = 1}^{\infty} ({(- 1)}^{r + 1} / r) \sum h_{1}^{+} . . . h_{r}^{+}$ is primitive, where $\sum h_{1} \otimes . . . \otimes h_{r} = Δ_{r - 1} (h)$ .

An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro (2011)

Annales de l’institut Fourier

Similarity:

A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ( $ϕ, Γ$ )-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ( $ϕ, Γ$ )-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas...

Complete filtered Lie algebras over a vector space of dimension two.

Judson, Thomas W. (2002)

Journal of Lie Theory

Similarity:

An introduction to constructive algebraic analysis and its applications

Alban Quadrat (2010)

Les cours du CIRM

Similarity: