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The K THEORY of the PROJECTIVE UNITARY GROUPS Let U Ams Form
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People also ask
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What is the K-theory of groups?
The K-theory groups can be computed using the stable homotopy type of the space, which provides a way to simplify complex topological problems. K-theory exhibits functorial properties, meaning it can be applied consistently across various topological spaces and morphisms.
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What is the quotient set of cosets?
A quotient group is the set of cosets of a normal subgroup of a group. Let N be a normal subgroup of group G. If x be any arbitrary element in G, then Nx is a right coset of N in G, and xN is a left coset of N in G.
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What is a unitary group?
Generally, a unitary business group is a group of related persons whose business activities or operations are interdependent. More specifically, a unitary business group is two or more persons that satisfy both a control test and one of two relationship tests.
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Why is K-theory called K-theory?
K-theory is a relatively new mathematical term. Its origins in the late 1950s go back to Alexander Grothendieck. He used the letter 'K' for 'Klasse', which means 'class' in German, his mother tongue, as the letter 'C' was already used elsewhere, for example for function spaces.
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What is the quotient of the unitary group?
The quotient of the unitary group by its center is called the projective unitary group, PU(n, q2), and the quotient of the special unitary group by its center is the projective special unitary group PSU(n, q2).
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What is the order of the unitary group?
In a paper of Wall (page 33), it is mentioned that the order of this group is q(n2−n)/2n∏i=1(qi−(−1)i).
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What is the quotient of a group?
In case you'd like a little refresher, here's the definition: Definition: Let G be a group and let N be a normal subgroup of G . Then G/N={gN:g∈G} G / N = { g N : g ∈ G } is the set of all cosets of N in G and is called the quotient group of N in G .
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