skew-commutative
|skew-com-mu-ta-tive|
/skjuː-kəˈmjuːtɪv/
commute up to a sign
Etymology
'skew-commutative' originates from Modern English as a compound of 'skew' and 'commutative'; 'skew' (from Old Norse/Scots via Middle English) meant 'oblique, not straight or symmetric', and 'commutative' comes from Latin 'commutare' (com- 'together' + mutare 'to change, exchange').
'skew-commutative' developed as a mathematical compound phrase in Modern English (initially written as 'skew commutative' or 'skew commutativity' in technical texts) and later stabilized in usage as the hyphenated adjective 'skew-commutative' to describe graded or sign-twisted commutativity.
Initially the components suggested 'oblique' + 'exchange'; in mathematics the compound acquired the specialized meaning 'commute up to a sign determined by degree' (a technical sense rather than a literal 'oblique commutativity').
Meanings by Part of Speech
Adjective 1
describing a (typically graded) algebraic product for which swapping two homogeneous elements multiplies the result by a sign determined by their degrees; formally, for homogeneous elements a,b one has ab = (-1)^{|a||b|}ba.
The exterior algebra is a skew-commutative graded algebra: for homogeneous elements x and y, xy = (-1)^{|x||y|}yx.
Synonyms
Antonyms
Last updated: 2025/10/22 06:46