# Symplectic

Symplectic may refer to:

in Mathematics:

• Symplectic Clifford algebra, see Weyl algebra
• Symplectic geometry
• Symplectic group
• Symplectic integrator
• Symplectic manifold
• Symplectic matrix
• Symplectic representation
• Symplectic vector space

in Biology:

• Symplectic bone, a bone found in fish skulls

### Other articles related to "symplectic":

Almost Symplectic Manifold
... In differential geometry, an almost symplectic structure on a differentiable manifold M is a two-form ω on M which is everywhere non-singular ... If, in addition, ω is closed, then it is a symplectic form ... An almost symplectic manifold is an Sp-structure requiring ω to be closed is an integrability condition ...
Symplectic Representation
... equivalently a group or Lie algebra homomorphism from G or g to the symplectic group Sp(V,ω) or its Lie algebra sp(V,ω) If G is a compact group (for example, a finite group), and F ... representations of finite or compact groups are often called symplectic representations, and may be identified using the Frobenius-Schur indicator ...
Classical Groups Over General Fields or Rings - Symplectic Groups
... The symplectic group Sp2n(R) preserves a skew symmetric form on a module ... It has a quotient, the projective symplectic group PSp2n(R) ... The general symplectic group GSp2n(R) consists of the automorphisms of a module multiplying a skew symmetric form by some invertible scalar ...
Symplectic Sum - History and Applications
... The symplectic sum was first clearly defined in 1995 by Robert Gompf ... to demonstrate that any finitely presented group appears as the fundamental group of a symplectic four-manifold ... Thus the category of symplectic manifolds was shown to be much larger than the category of Kähler manifolds ...