Related papers: Unital versions of the higher order peak algebras

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

We describe extension classes arising in the $\ell$-adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that this description is consistent with the "plectic conjectures"…

Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

For $G$ a finite abelian group, we study the properties of general equivalence relations on $G_n=G^n\rtimes \SG_n$, the wreath product of $G$ with the symmetric group $\SG_n$, also known as the $G$-coloured symmetric group. We show that…

Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…

We extend in this paper several results of E. Kirchberg, S. Wassermann and the author dealing with continuous fields of C*--algebras to the semi-continuous case. We provide a new characterisation of separable lower semi-continuity…

We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.

Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs with coefficients in a…

We classify unital associative conformal algebras of linear growth and provide new examples of such.

We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this…

We extend Ueda's peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras, to sigma-finite von Neumann algebras (that is, von Neumann algebras with a faithful state; which includes those on a separable Hilbert…

Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher lift of Schur's P-functions and a right coideal subalgebra of the Poirier-Reutenauer algebra is…

We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the…

The algebra B of bicomplex numbers is viewed as a complexification of the Archimedean f-algebra of hyperbolic numbers D. This lattice-theoretic approach allows us to establish new properties of the so-called D-norms. In particular, we show…

We classify the real subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$, a non-compact real form of the complex special linear algebra $\mathfrak{sl}_3(\mathbb{C})$. Our approach combines Galois cohomology with the…

By means of a generalization of the S-expansion method we construct a procedure to obtain expanded higher-order Lie algebras. It is shown that the direct product between an Abelian semigroup S and a higher-order Lie algebra…

We find a remarkable subalgebra of higher symmetries of the elliptic Euler-Darboux equation. To this aim we map such equation into its hyperbolic analogue already studied by Shemarulin. Taking into consideration how symmetries and recursion…

This article is devoted to the investigation of $B^*$-algebras, dual and annihilator ultranormed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and using them core radicals and radicals…

It was once conjectured that if $A$ is a uniform algebra on its maximal ideal space $X$, and if each point of $X$ is a peak point for $A$, then $A = C(X)$. This peak-point conjecture was disproved by Brian Cole in 1968. Here we establish a…