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I am unsure about a canonical meaning of this notion. On one hand the WP-article about anticommutativity seems to refer to the algebraic notion of groups, involving an operation denoted by "∗", but without being explicit about the identitity and the notation of inverse elements for this assumed group. There is just the unexplained use of "-" and a sgn-operator (applied to permutations of indices).
On the other hand I have a vague image about an anticommutative binary Lie-bracket, defined on a k-module over some unitary ring k, involving the additive inverses of the group structure in the module, when commuting the operands of the bracket.
Does one need two operations (k-algebra + module group) or not (group alone)? In case of two, which operation necessarily supplies the relevant inverse? Are there several definitions of "anticommutativity", or are the above sketched situations in some way congruent? Purgy ( talk) 17:05, 9 March 2018 (UTC)
Mathematics desk | ||
---|---|---|
< March 8 | << Feb | March | Apr >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I am unsure about a canonical meaning of this notion. On one hand the WP-article about anticommutativity seems to refer to the algebraic notion of groups, involving an operation denoted by "∗", but without being explicit about the identitity and the notation of inverse elements for this assumed group. There is just the unexplained use of "-" and a sgn-operator (applied to permutations of indices).
On the other hand I have a vague image about an anticommutative binary Lie-bracket, defined on a k-module over some unitary ring k, involving the additive inverses of the group structure in the module, when commuting the operands of the bracket.
Does one need two operations (k-algebra + module group) or not (group alone)? In case of two, which operation necessarily supplies the relevant inverse? Are there several definitions of "anticommutativity", or are the above sketched situations in some way congruent? Purgy ( talk) 17:05, 9 March 2018 (UTC)