Some articles on algebras, algebra:
Statistical Dependence - Definition - Independent σ-algebras
... by the following definition of independence for σ-algebras ... Let (Ω, Σ, Pr) be a probability space and let A and B be two sub-σ-algebras of Σ ... B are said to be independent if, whenever A ∈ A and B ∈ B, Likewise, a finite family of σ-algebras is said to be independent if and only if for all and an infinite family of σ-algebras is said to be ...
... by the following definition of independence for σ-algebras ... Let (Ω, Σ, Pr) be a probability space and let A and B be two sub-σ-algebras of Σ ... B are said to be independent if, whenever A ∈ A and B ∈ B, Likewise, a finite family of σ-algebras is said to be independent if and only if for all and an infinite family of σ-algebras is said to be ...
Moufang Polygon - Quadrangular Algebras
... A potential use for quadrangular algebras is to analyze two open questions ... For the E8 hexagons this can be rephrased as a question on quadratic Jordan algebras, and for the E8 quadrangles it can now be rephrased in terms of quadrangular algebras ...
... A potential use for quadrangular algebras is to analyze two open questions ... For the E8 hexagons this can be rephrased as a question on quadratic Jordan algebras, and for the E8 quadrangles it can now be rephrased in terms of quadrangular algebras ...
Capelli's Identity - Generalizations
... Most of them are based on the Lie algebra point of view ... Such generalizations consist of changing Lie algebra to simple Lie algebras and their super (q), and current versions ... that the identity is intimately related with semi-simple Lie algebras ...
... Most of them are based on the Lie algebra point of view ... Such generalizations consist of changing Lie algebra to simple Lie algebras and their super (q), and current versions ... that the identity is intimately related with semi-simple Lie algebras ...
Cylindric Algebra
... The notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic with equality ... This is comparable to the role Boolean algebras play for propositional logic ... Indeed, cylindric algebras are Boolean algebras equipped with additional cylindrification operations that model quantification and equality ...
... The notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic with equality ... This is comparable to the role Boolean algebras play for propositional logic ... Indeed, cylindric algebras are Boolean algebras equipped with additional cylindrification operations that model quantification and equality ...
Beyond Superstring Theory - Kac–Moody Algebras
... the symmetry used to describe string theory is based on infinite dimensional Lie algebras ... Some Kac–Moody algebras that have been considered as symmetries for M-theory have been E10 and E11 and their supersymmetric extensions ...
... the symmetry used to describe string theory is based on infinite dimensional Lie algebras ... Some Kac–Moody algebras that have been considered as symmetries for M-theory have been E10 and E11 and their supersymmetric extensions ...
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