Related papers: Irredundant Sets in Atomic Boolean Algebras

In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the…

We give an alternative construction of the essential $C^*$-algebra of an \'etale groupoid, along with an ``amenability'' notion for such groupoids that is implied by the nuclearity of this essential $C^*$-algebra. In order to do this we…

Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is…

We modify the Hochschild $\phi$-map to construct central extensions of a restricted Lie algebra. Such central extension gives rise to a group scheme which leads to a geometric construction of unrestricted representations. For a classical…

Let G be a complex simple algebraic group. We consider invariant-theoretic properties of the simple G-module whose highest weight is the short dominant root.

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…

The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…

Let $L^1_\om(G)$ be a Beurling algebra on a locally compact abelian group $G$. We look for general conditions on the weight which allows the vanishing of continuous derivations of $L^1_\om(G)$. This leads us to introducing vector-valued…

The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…

An irredundant base of a group $G$ acting faithfully on a finite set $\Gamma$ is a sequence of points in $\Gamma$ that produces a strictly descending chain of pointwise stabiliser subgroups in $G$, terminating at the trivial subgroup.…

In this article, we give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of Lie groups defined by T.Robart [13], we define the closed holonomy group of a…

We classify all equivalences between the indecomposable abelian categories which appear as blocks in BGG category O for reductive Lie algebras. Our classification implies that a block in category O only depends on the Bruhat order of the…

Let G be a connected semisimple algebraic group over $k$, with Lie algebra $\g$. Let $\h$ be a subalgebra of $\g$. A simple finite-dimensional $\g$-module V is said to be $\h$-indecomposable if it cannot be written as a direct sum of two…

A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations.…

A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…

Let $G$ be a connected real algebraic group. An unrefinable chain of $G$ is a chain of subgroups $G=G_0>G_1>...>G_t=1$ where each $G_i$ is a maximal connected real subgroup of $G_{i-1}$. The maximal (respectively, minimal) length of such an…

For suitable groups G we will show that one can add a Boolean algebra B by forcing in such a way that Aut(B) is almost isomorphic to G. In particular, we will give a positive answer to the following question due to J.Roitman: Is…

The idea that the cohomology of finite groups might be fruitfully approached via the cohomology of ambient semisimple algebraic groups was first shown to be viable in the papers [CPS75] and [CPSvdK77]. The second paper introduced, through a…

We give a combinatorial description of a family of indecomposable objects in the bounded derived categories of a new class of algebras: string almost gentle algebras. These indecomposable objects are, up to isomorphism, the string and band…