Dimension Free and Infinite Variance Tail Estimates on Poisson Space

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including Lévy’s stochastic area and the square norm of Brownian paths. In the infinite variance case, various tail estimates such as stable ones are also presented.      

On Spencer Cohomologies of Affine Algebraic Varieties

This paper contains proofs and examples for some key facts about algebraic Spencer cohomologies preannounced elsewhere. The author hopes that here he has managed to build a more systematic discourse of the issues raised in earlier works.     

Commutative cancellative semigroups of finite rank

The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for N-semigroups.     

格蕴涵代数与BCK代数的关系

本文给出了有界可换的ＢＣＫ代数的分配性的一些等价条件，指出了格蕴涵代数与有界可换分配的ＢＣＫ代数以及格Ｈ蕴涵代数与有界关联的ＢＣＫ代数之间的对偶关系     

Real stable ranks

Several new notions of stable ranks for commutative Banach algebras are introduced. Due to the fact that they depend on certain orthogonal groups, they are called real stable ranks and are finer than their complex counterparts.     

On para‐Kähler Lie algebroids and contravariant pseudo‐Hessian structures

In this paper, we generalize all the results obtained on para‐Kähler Lie algebras in [3] to para‐Kähler Lie algebroids. In particular, we study exact para‐Kähler Lie algebroids as a generalization of exact para‐Kähler Lie algebras. This study leads to a natural generalization of pseudo‐Hessian manifolds, we call them contravariant pseudo‐Hessian manifolds. Contravariant pseudo‐Hessian manifolds have many similarities with Poisson manifolds. We explore these similarities which, among others, leads to a powerful machinery to build examples of non trivial pseudo‐Hessian structures. Namely, we will show that given a finite dimensional commutative and associative algebra , the orbits of the action Φ of on given by are pseudo‐Hessian manifolds, where . We illustrate this result by considering many examples of associative commutative algebras and show that the resulting pseudo‐Hessian manifolds are very interesting.     

Symmetries of the Partial Order of Traces

This paper deals with the automorphism group of the partial order of finite traces. We show that any group can arise as such an automorphism group if we allow arbitrary large dependence alphabets. Restricting to finite dependence alphabets, the automorphism groups are profinite and possess only finitely many simple decomposition factors. Finally, we show that the partial order associated with the Rado graph as dependence alphabet does not give rise to a homogeneous domain thereby answering an open question from Boldi, P., Cardone, F. and Sabadini, N. (1993).     

Birational extensions of a noetherian UFD

We construct two nonisomorphic groups G and Q of order 96 which have isomorphic tables of marks, but such that the centre of G has order 8 and the centre of Q has order 4. We also note that G has an abelian subgroup of order 48, whereas Q has no abelian subgroup of that order. This also leads us to conclude that this isomorphism of tables of marks does not preserve normalizers.     

Givental group action on topological field theories and homotopy Batalin–Vilkovisky algebras

In this paper, we initiate the study of the Givental group action on Cohomological Field Theories in terms of homotopical algebra. More precisely, we show that the stabilisers of Topological Field Theories in genus 0 (respectively in genera 0 and 1) are in one-to-one correspondence with commutative homotopy Batalin–Vilkovisky algebras (respectively wheeled commutative homotopy BV-algebras).