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The composition of the braids σ and τ is written as στ.. The set of all braids on four strands is denoted by .The above composition of braids is indeed a group operation. . The identity element is the braid consisting of four parallel horizontal strands, and the inverse of a braid consists of that braid which "undoes" whatever the first braid did, which is obtained by flipping a diagram ...
When a mental state is shared by a large proportion of the members of a group or society, it can be called a collective mental state. Gustave Le Bon proposed that mental states are passed by contagion, while Sigmund Freud wrote of war fever in his work Group Psychology and the Analysis of the Ego (1922), a perfect example of the collective ...
In the mathematical area of braid theory, the Dehornoy order is a left-invariant total order on the braid group, found by Patrick Dehornoy. [1] [2] Dehornoy's original discovery of the order on the braid group used huge cardinals, but there are now several more elementary constructions of it. [3]
They are closely related with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin–Tits groups, among others. The groups are named after Emil Artin, due to his early work on braid groups in the 1920s to 1940s, [1] and Jacques Tits who developed the theory of a more general class of groups in the ...
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The category of representations of a group (or a Lie algebra) is a symmetric monoidal category where () =. The category of representations of a quantized universal enveloping algebra U q ( g ) {\displaystyle U_{q}({\mathfrak {g}})} is a braided monoidal category, where γ {\displaystyle \gamma } is constructed using the universal R -matrix .
[7] [8] Also, a process of identification with the aggressor can take place, for example, as happens in regression. Thus, Freud came to the conclusion: "A primary mass is a number of individuals who have put one and the same object in place of their ego ideal and consequently identify with each other."
A large body of research in meaningful 'real-world' contexts lends support to the applicability of the common ingroup identity model. In a diverse range of intergroup situations, it has been demonstrated that the conditions specified by the contact hypothesis (i.e. cooperative interaction) reduce intergroup bias through transforming members' representations of separate group memberships to one ...