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Pin group

Index Pin group

In mathematics, the pin group is a certain subgroup of the Clifford algebra associated to a quadratic space. [1]

23 relations: Andrzej Trautman, Back-formation, Clifford algebra, Commutative diagram, Connected space, Covering group, Covering space, Dicyclic group, Dihedral group, Indefinite orthogonal group, Jean-Pierre Serre, Mathematics, Orthogonal group, Point reflection, Princeton University Press, Principal homogeneous space, Projective orthogonal group, Quadratic form, Reflection (mathematics), Rotation, Spin group, Topological group, Topology (journal).

Andrzej Trautman

Andrzej Mariusz Trautman (born January 4, 1933) is a Polish mathematical physicist who has made contributions to classical gravitation in general and to general relativity in particular.

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Back-formation

In etymology, back-formation is the process of creating a new lexeme by removing actual or supposed affixes.

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Clifford algebra

In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra.

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Commutative diagram

The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result.

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Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

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Covering group

In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p: G → H is a continuous group homomorphism.

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Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

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Dicyclic group

In group theory, a dicyclic group (notation Dicn or Q4n) is a member of a class of non-abelian groups of order 4n (n > 1).

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Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

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Indefinite orthogonal group

In mathematics, the indefinite orthogonal group, is the Lie group of all linear transformations of an n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature, where.

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Jean-Pierre Serre

Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

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Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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Principal homogeneous space

In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial.

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Projective orthogonal group

In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V.

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Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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Rotation

A rotation is a circular movement of an object around a center (or point) of rotation.

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Spin group

In mathematics the spin group Spin(n) is the double cover of the special orthogonal group, such that there exists a short exact sequence of Lie groups (with) As a Lie group, Spin(n) therefore shares its dimension,, and its Lie algebra with the special orthogonal group.

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Topological group

In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.

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Topology (journal)

Topology was a peer-reviewed mathematical journal covering topology and geometry.

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Redirects here:

Pin(n), Pinor.

References

[1] https://en.wikipedia.org/wiki/Pin_group

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