in context with group theory I came across the term 'invariant subalgebra' which says: some generators of group G which goes either into itself or zero under commutation with any element of the whole algebra.
Can anyone please elucidate an example?
http://math.stackexchange.com/questions/644504/invariant-subalgebra-of-a-lie-algebra-under-an-automorphism-of-the-dynkin-diagra
This is a good question with many possible answers. In addition to the helpful answer already given, there is a bit more to consider.
See,for example:
http://arxiv.org/pdf/math/0103047.pdf
and
http://arxiv.org/pdf/hep-th/0004058.pdf
Let V be an algebra and W is a subalgebra of V. Then W is called an invariant subalgebra of V if for any algebra homomorphism T : V → V, we have T(W) ⊆ W. For example, (i) W= Ker(T) is invariant, (ii) V and {0} are trivial invariant subspaces.
CONSIDER THE ALGEBRAIC SYSTEM NEAR-RING.
Def.2.2.1 on page 108 of the book (NEAR RINGS , FUZZY IDEALS, AND GRAPH THEORY, (Authors: Bhavanari Satyanarayana and Kuncham Syam Prasad) (Publisher: CRC Press, Taylor and Francis Group, England, 2013).
This definition explained the concepts: LEFT INVARIANT SUBNEAR-RING, RIGHT INVARIANT NEAR-RING, INVARIANT SUBNEAR-RING.
Def.3.3.5 (II) on page 147 of the book (NEAR RINGS , FUZZY IDEALS, AND GRAPH THEORY, (Authors: Bhavanari Satyanarayana and Kuncham Syam Prasad) (Publisher: CRC Press, Taylor and Francis Group, England, 2013).
This definition explained the concept: INVARIANT SEQUENCE
Def.8.4.4. on page 345 of the book (NEAR RINGS , FUZZY IDEALS, AND GRAPH THEORY, (Authors: Bhavanari Satyanarayana and Kuncham Syam Prasad) (Publisher: CRC Press, Taylor and Francis Group, England, 2013).
This definition explained the concept: H- INVARIANT FUZZY SET
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