Word Pronunciation & Dictionary

symplectic group

Word Rarity Very rare

Frequency: Zipf frequency 2.01 in modern English

Syllables: sym-plec-tic -group
IPA

29

Scrabble Score

15

Letters

4

Syllables

13

Unique Chars

Meaning

noun

For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F.

Example Sentences

"This representation ω arises by virtue of the existence of an action by automorphisms of the symplectic group on a certain two-step nilpotent group, commonly called the Heisenberg group. Weil was of course working in the adelic formalism of modern number theory, so he considered symplectic groups and Heisenberg groups with coefficients in a general local field."
"The exponential of an operator gives the exponential mapping #92;textstyleH#92;mapsto#92;text#123;exp#125;(H)#61;#92;sum#123;Hᵏ#47;k#33;#125; of the space of Hamiltonian operators to the symplectic group. The symplectic group acts by conjugation on itself and on its Lie algebra."
"The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group."

Etymology

So named by German mathematician Hermann Weyl, replacing previous confusing names. More at symplectic.

Inflected Forms

symplectic groups (plural)

Phrases

compact symplectic group

Questions

What does symplectic group mean?: For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F.
Where does symplectic group come from?: So named by German mathematician Hermann Weyl, replacing previous confusing names. More at symplectic.

How to pronounce symplectic group

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