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Longer chains of idempotents in βG

Neil Hindman, Dona Strauss, Yevhen Zelenyuk (2013)

Fundamenta Mathematicae

Given idempotents e and f in a semigroup, e ≤ f if and only if e = fe = ef. We show that if G is a countable discrete group, p is a right cancelable element of G* = βG∖G, and λ is a countable ordinal, then there is a strictly decreasing chain ⟨ q σ ⟩ σ < λ of idempotents in C p , the smallest compact subsemigroup of G* with p as a member. We also show that if S is any infinite subsemigroup of a countable group, then any nonminimal idempotent in S* is the largest element of such a strictly decreasing chain of idempotents....

Loops and quasigroups: Aspects of current work and prospects for the future

Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics.

Lp multipliers and their H1-L1 estimates on the Heisenberg group.

Chin-Cheng Lin (1995)

Revista Matemática Iberoamericana

We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.

Lp-estimates for the wave equation on the Heisenberg group.

Detlef Müller, Elias M. Stein (1999)

Revista Matemática Iberoamericana

Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α &gt; (d - 1) |1/p - 1/2|.

Lyapunov exponents for stochastic differential equations on semi-simple Lie groups

Paulo R. C. Ruffino, Luiz A. B. San Martin (2001)

Archivum Mathematicum

With an intrinsic approach on semi-simple Lie groups we find a Furstenberg–Khasminskii type formula for the limit of the diagonal component in the Iwasawa decomposition. It is an integral formula with respect to the invariant measure in the maximal flag manifold of the group (i.e. the Furstenberg boundary B = G / M A N ). Its integrand involves the Borel type Riemannian metric in the flag manifolds. When applied to linear stochastic systems which generate a semi-simple group the formula provides a diagonal matrix...

Lyapunov measures on effect algebras

Anna Avallone, Giuseppina Barbieri (2003)

Commentationes Mathematicae Universitatis Carolinae

We prove a Lyapunov type theorem for modular measures on lattice ordered effect algebras.

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