Central simple algebra information

areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A which is simple, and for which the center...

In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular...

classification of finite simple groups says that most finite simple groups arise as the group G(k) of k-rational points of a simple algebraic group G over a finite...

A central simple algebra over K is a matrix algebra over a (finite-dimensional) division algebra with center K. For example, the central simple algebras...

version for central simple algebras, as it appears in (Knapp 2007, p.115): Theorem: If A is a finite-dimensional central simple algebra over a field...

quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending...

are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist...

Birman–Wenzl algebra Boolean algebra Borcherds algebra Brauer algebra C*-algebra Central simple algebra Clifford algebra Cluster algebra Dendriform algebra Differential...

and classification of Lie groups in terms of Lie algebras, which are simpler objects of linear algebra. In more detail: for any Lie group, the multiplication...

theory Degree of unsolvability in recursion theory Degree of a central simple algebra Degree of a permutation group, the number of elements that are permuted...

module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field...

affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given...

(mathematics), Division ring, division algebra Simple ring, Central simple algebra, Semisimple ring, Semisimple algebra Primitive ring, Semiprimitive ring...

closer non-commutative analog are central simple algebras (CSAs) – ring extensions over a field, which are simple algebra (no non-trivial 2-sided ideals...

ring is −∞. The zero ring is semisimple but not simple. The zero ring is not a central simple algebra over any field. The total quotient ring of the zero...

In mathematics, an Azumaya algebra is a generalization of central simple algebras to R {\displaystyle R} -algebras where R {\displaystyle R} need not...

of unity. An Okubo algebra is an algebra constructed in this way from the trace-zero elements of a degree-3 central simple algebra over a field. Unital...

crossed product algebra A is a central simple algebra (CSA) of degree equal to [L : K]. The converse holds: every central simple algebra over K that splits...

in a strictly larger subfield of A. If A is a finite-dimensional central simple algebra, then a subfield E of A is called a strictly maximal subfield if...

classifying all quadratic forms over k or all central simple algebras over k. These problems are easy for k algebraically closed, and they are understood for some...

(identity matrix) as the unity. Central simple algebra Clifford algebra Hurwitz's theorem (normed division algebras) Generic matrix ring Sylvester's...

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