This open access textbook presents a comprehensive treatment of the arithmetic theory of
quaternion algebras and orders, a subject with applications in diverse areas of mathematics …

We review the recently established relationships between black hole entropy in string theory
and the quantum entanglement of qubits and qutrits in quantum information theory. The first …

We review various aspects of de Sitter spacetime in string theory: its status as an Effective
Field Theory spacetime solution, its relation to the vacuum energy problem in string theory …

In this chapter, we begin by introducing the simplest type of manifolds, the topological
manifolds, which are topological spaces with three special properties that encode what we …

An important concept in physics is that of symmetry, whether it be rotational symmetry for
many physical systems or Lorentz symmetry in relativistic systems. In many cases, the group …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

This book investigates the geometry of quaternion and octonion algebras. Following a
comprehensive historical introduction, the book illuminates the special properties of 3-and 4 …

The theory of slice regular functions (originally Cullen-regular functions) was born at George
Mason University, in Virginia, where the first and third authors collaborated for a 2-month …