In this article we explore to what extend the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] the authors establish an isomorphism between Hamiltonian Floer homology and singular homology of the underlying symplectic manifold. In general, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian su...

Abstract. We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees and binary sequences. On the combinatorial side, we study the rotation lattices on permutrees and their lattice homomorphisms, unifying the weak order, Tamari, Cambrian and boolean lattices and the classical maps between them. On the geometric side, we provide both the vertex and facet descriptions...

There are excellent accounts on automatic continuity theory in the associative context. Since there have been a number of advances in automatic continuity theory in the nonassociative context, it seems to be an opportune time to present a comprehensive discussion of the currently known results on automatic continuity of linear maps in this context. These notes are an attempt to collect together...

In this paper, we describe linear maps between complex Banach algebras that preserve products equal to fixed elements. This generalizes some important special cases where the elements are zero or identity element. First show if such map preserves a finite-rank operator, then it must also product. several instances, is enough product preserving be scalar multiple of an algebra homomorphism. Seco...

Let S(r) denote the w-sphere with a linear involution having a fixed point set of codimension r, where O ^ r ^ w . We pick some fixed point as a base point and consider the set [S(r); S(t)] of base point preserving equivariant homotopy classes of maps from S(r) to S(t). This has a natural group structure for n—r^l and is abelian if n—r^2. There is a suspension functor S without action and one 2...

Employing the algebraic framework of local quantum physics,vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding state a continuous unitary representation of the proper Poincaré group which acts covariantly on the net and leaves the state invariant. The p...

Employing the algebraic framework of local quantum physics,vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding state a continuous unitary representation of the proper Poincaré group which acts covariantly on the net and leaves the state invariant. The p...

Let G be a finite group, and let V and W be finite-dimensional real orthogonal G-modules with V 3 W, and with unit spheres S(V) and S( W) respectively. The purpose of this note is to give necessary sufficient conditions for the existence of a C-map /: S( V) -» S( W) in terms of the Burnside ring of G and its relationship with V and W. Note that if W has a nonzero fixed point, such a G-map alway...

Let [Formula: see text] and be two alternative ∗-algebras with identities text], respectively, nontrivial symmetric idempotents in text]. In this paper, we study the characterization of multiplicative ∗-Lie-type maps. As application, get a result on text]-algebras.

Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists, compatible with adjacent homomorphisms, give rise to gauge transformation of twisted homomorphisms, which behave nicely with respect to compositions. Here we s...