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Multiple antisymmetry

In crystallography and materials science multiple antisymmetry is the concept of a substance possessing two or more different types of antisymmetry simultaneously.

Version
v1 · 2026-09-28 · History
Domain-specific #
10851
Domain group
Natural Sciences
Origin domain
Chemistry & Materials Science
Subdomains
Crystallography, Symmetry Theory → Chemistry & Materials Science

Core Idea

Multiple antisymmetry is treated here as the recurring crossdomainmodelsstructuresrepresentations identity summarized by this source-grounded definition: In crystallography and materials science multiple antisymmetry is the concept of a substance possessing two or more different types of antisymmetry simultaneously. In crystallography and materials science multiple antisymmetry is the concept of a substance possessing two or more different types of antisymmetry simultaneously. Multiple antisymmetry has applications in the fields of magnetic structures, ferroelectricity, and the physical properties of crystals. Where there are l different types of antisymmetry operations the total number of antisymmetry combinations is 2^l -1.

Scope of Application

  • Multiple antisymmetry. If two different antisymmetry operations are defined (for example 1' and 1^ ) they can be used to generate double antisymmetry groups.

  • Applications. Zamorzaev, practical applications of double antisymmetry were being pursued by other Russian researchers such as B.

  • Applications. Belov used two different types of antisymmetry to describe the combination of ferromagnetic and ferroelectric properties of crystals.

  • Applications. Shaskolskaya in 1982, and was used to derive the ferroelectric space groups in 1986.

  • Applications. Rotation-reversal space groups have been used in the classification of tilted octahedra perovskites.

Clarity

A clear use of Multiple antisymmetry names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In crystallography and materials science multiple antisymmetry is the concept of a substance possessing two or more different types of antisymmetry simultaneously.

Manages Complexity

Multiple antisymmetry compresses multiple crossdomainmodelsstructuresrepresentations details into a stable diagnostic relation. The source shows both the central mechanism—space-time reversal (inverting both space and time coordinates, signified by \overline{1} ' ) was discussed by Yu.—and the practical consequence—a few papers on multiple antisymmetry were also published by non-Russian authors. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.

Abstract Reasoning

  1. Type the carrier. Identify the crossdomainmodelsstructuresrepresentations entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In crystallography and materials science multiple antisymmetry is the concept of a substance possessing two or more different types of antisymmetry simultaneously.
  3. Check operation and conditions. The combination of space reversal and magnetic reversal was studied by Vojtěch Kopský in 2006.
  4. Demand recognition evidence. The first suggestion of the concept of multiple antisymmetry was in a 1944 paper by Alexei Vasilievich Shubnikov.
  5. Test variation.

Knowledge Transfer

Within the home domain. Knowledge about Multiple antisymmetry transfers literally when a new case preserves the same carrier type, relation, and recognition test. If two different antisymmetry operations are defined (for example 1' and 1^ ) they can be used to generate double antisymmetry groups. Zamorzaev, practical applications of double antisymmetry were being pursued by other Russian researchers such as B. Beyond the home domain. No canonical parent is asserted for Multiple antisymmetry.

Neighborhood in Abstraction Space

Multiple antisymmetry sits in a sparse region of the domain-specific corpus (85th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Named Physical Phenomena & Theoretical Constructs (16 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08