**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

... 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

... 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

... 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 ...Main Site Subjects

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