Regular representationIn mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself by translation. One distinguishes the left regular representation λ given by left translation and the right regular representation ρ given by the inverse of right translation. Representation theory of finite groups#Left- and right-regular representation For a finite group G, the left regular representation λ (over a field K) is a linear representation on the K-vector space V freely generated by the elements of G, i.
WomanA woman is an adult female human. Prior to adulthood, a female human is referred to as a girl (a female child or adolescent). The plural women is sometimes used in certain phrases such as "women's rights" to denote female humans regardless of age. Typically, women inherit a pair of X chromosomes, one from each parent, and are capable of pregnancy and giving birth from puberty until menopause. More generally, sex differentiation of the female fetus is governed by the lack of a present, or functioning, SRY-gene on either one of the respective sex chromosomes.
Group actionIn mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.
VikingsVikings is the modern name given to seafaring people originally from Scandinavia (present-day Denmark, Norway and Sweden), who from the late 8th to the late 11th centuries raided, pirated, traded and settled throughout parts of Europe. They also voyaged as far as the Mediterranean, North Africa, Volga Bulgaria, the Middle East, and North America. In their countries of origin, and some of the countries they raided and settled in, this period is popularly known as the Viking Age, and the term "Viking" also commonly includes the inhabitants of the Scandinavian homelands as a whole.
Group theoryIn abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Creation scienceCreation science or scientific creationism is a pseudoscientific form of Young Earth creationism which claims to offer scientific arguments for certain literalist and inerrantist interpretations of the Bible. It is often presented without overt faith-based language, but instead relies on reinterpreting scientific results to argue that various myths in the Book of Genesis and other select biblical passages are scientifically valid.
Creation mythA creation myth or cosmogonic myth is a type of cosmogony, a symbolic narrative of how the world began and how people first came to inhabit it. While in popular usage the term myth often refers to false or fanciful stories, members of cultures often ascribe varying degrees of truth to their creation myths. In the society in which it is told, a creation myth is usually regarded as conveying profound truths - metaphorically, symbolically, historically, or literally.
Reductive groupIn mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n).
Dihedral groupIn mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, D_n or Dih_n refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D_2n refers to this same dihedral group.
