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The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold

Jonathan Pridham (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...

The pseudovariety of semigroups of triangular matrices over a finite field

Jorge Almeida, Stuart W. Margolis, Mikhail V. Volkov (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.

The quantum duality principle

Fabio Gavarini (2002)

Annales de l’institut Fourier

The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors 𝒬 𝒰 ℰ 𝒜 ⟶ 𝒬 ℱ 𝒮 ℋ 𝒜 and 𝒬 ℱ 𝒮 ℋ 𝒜 ⟶ 𝒬 𝒰 ℰ 𝒜 , inverse to...

The 𝒜 r -free products of archimedean l -groups

Dao Rong Tong (1998)

Czechoslovak Mathematical Journal

The objective of this paper is to give two descriptions of the 𝒜 r -free products of archimedean ℓ -groups and to establish some properties for the 𝒜 r -free products. Specifically, it is proved that 𝒜 r -free products satisfy the weak subalgebra property.

The rank of a commutative semigroup

Antonio M. Cegarra, Mario Petrich (2009)

Mathematica Bohemica

The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups S by defining rank S as the supremum of cardinalities of finite independent subsets of S . Representing such a semigroup S as a semilattice Y of (archimedean) components S α , we prove that rank S is the supremum of ranks of various S α . Representing a commutative separative semigroup S as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations...

The rate of escape for random walks on polycyclic and metabelian groups

Russ Thompson (2013)

Annales de l'I.H.P. Probabilités et statistiques

We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...

The ratio and generating function of cogrowth coefficients of finitely generated groups

Ryszard Szwarc (1998)

Studia Mathematica

Let G be a group generated by r elements g 1 , … , g r . Among the reduced words in g 1 , … , g r of length n some, say γ n , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of γ 2 n has a limit, called the cogrowth exponent with respect to the generators g 1 , … , g r . We show by analytic methods that the numbers γ n vary regularly, i.e. the ratio γ 2 n + 2 / γ 2 n is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated...

Currently displaying 501 – 520 of 855