Related papers: Notes on normed algebras, 4

Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…

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…

We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…

We study normed groupoids with dilations and their induced deformations.

This short survey, which was written to accompany a minicourse at the BIRS conference "Topology in dimension 4.5", concerns invariants of knotted $2$-spheres in $S^4$, also known as $2$-knots. It covers invariants extracted from the…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the…

This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains.

In this revised version, we add some expository material and references and make some minor corrections.

Based on invariant algebras, we introduce representations$^{6-th}$ of Lie algebras and representations$^{< 4-th>}$ of Leibniz algebras, give the extended P-B-W Theorems in the context of the new representations of Lie algebras and Leibniz…

In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…

In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…

Combinatorial and topological aspects of monoids with an absorbing element and their associated algebras are considered. Phd thesis.

Notes on Commutative Alegbra and Algebraic Geometry covering rings, ideals, modules, presheaves, sheaves, schemes, homological algebra, \'etale cohomology and further topics that are more advanced.

The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.

This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…

This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…

In this paper we give a classification of classes of involutions on an automorphism group of an octonion algebra over fields of characteristic 2, and describe the classes of their fixed point groups.