Antipode, Antipodes, or Antipodeans may refer to:

  • Antipodal point, the diametrically opposite point on a sphere
  • Antipodes, the region on the Earth's surface which is diametrically opposite to another region
  • Antipodes Water Company, a premium bottled water brand
  • Antipode (algebra), the convolution inverse of the identity on a Hopf algebra
  • Antipode (chemistry), a synonym for the term enantiomer
  • Antipodes (submarine), a commercial submarine built in 1973
  • Antipodes (mental state), a concept in the essay Heaven and Hell by Aldous Huxley
  • Antipodes Islands, inhospitable volcanic islands
  • The Antipodes, a Caroline-era stage play by Richard Brome
  • Antipodeans, inhabitants of Australia, New Zealand and South Africa, see Antipodes
  • Antipodeans, 20th-century Australian art group
  • Antipodes (sculpture) by Jim Sanborn
  • Antipodean (cat), a breed of domestic cat
  • Antipode (journal), an academic journal and related blog
  • The Antipodean, an Australian illustrated periodical first published from 1892 to 1980
  • Antipode, a circus skill that involves juggling with one's feet while lying on one's back; a form of equilibristics

Other articles related to "antipode":

Tensor Algebra - Coalgebra Structures - Bialgebra and Hopf Algebra Structure
... Finally, the tensor algebra becomes a Hopf algebra with antipode given by extended linearly to all of TV ... on by and then extends to via Similarly one defines the antipode on by and then extends the antipode as the unique antiautomorphism of with this property, i.e ... we define the antipode on via ...
Hopf Algebras - Formal Definition - Properties of The Antipode
... The antipode S is sometimes required to have a K-linear inverse, which is automatic in the finite-dimensional case, or if H is commutative or cocommutative (or ... If a bialgebra B admits an antipode S, then S is unique ("a bialgebra admits at most 1 Hopf algebra structure") ... The antipode is an analog to the inversion map on a group that sends g to g-1 ...
Antipode (journal)
... Antipode A Radical Journal of Geography is a peer-reviewed academic journal and related website/blog that covers the field of critical geography. 1985 and today is owned and operated by the Antipode Foundation, a charity registered in England and Wales (no ... Antipode also publishes short commentaries (or 'Interventions' these meditate on the state of radical practice and/or theory, cast a radical geographer's eye over 'live' events, or ...
Hopf Algebra - Formal Definition - Hopf Subalgebras
... subalgebra if it is a subcoalgebra of H and the antipode S maps A into A ... the multiplication, comultiplication, counit and antipode of H is restricted to A (and additionally the identity 1 of H is required to be in A) ... The two conditions of normality are equivalent if the antipode S is bijective, in which case A is said to be a normal Hopf subalgebra ...