Notation question: like a direct product

In summary, the conversation is about a notation in a math text that resembles a direct product. The symbol is a multiplication X with a vertical line connecting the two left side ends, and the context of the conversation can be seen in an online preview of the text being read. The symbol is possibly a semidirect product and the LaTex commands for it are listed in the article.
  • #1
pellman
684
5
I am coming across a notation in a math text whose form and context suggest it is something like a direct product. The symbol is a multiplication X with a vertical line connecting the two left side ends. Can someone identify this symbol please?

The context can be seen here http://books.google.com/books?id=3J...CQrZcB&sa=X&oi=book_result&ct=result&resnum=1 2/3rds the way down on the page. This is an online preview of the text I am reading.
 
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  • #3
Hurkyl to the rescue again. That is it.

And look. The article lists the LaTex commands. [tex]
G = R^4 \ltimes SL(2,C)
[/tex]
 
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What is the meaning of "direct product" in mathematical notation?

The direct product is a mathematical operation that combines two or more mathematical objects (such as sets, groups, or vector spaces) into a single object. The resulting object contains all possible combinations of elements from the original objects.

How is the direct product denoted in mathematical notation?

The direct product is denoted by the symbol × or ⊗, or sometimes by the phrase "direct product". For example, the direct product of two sets A and B is written as A × B or A ⊗ B.

What are some common properties of the direct product?

The direct product obeys the associative and commutative properties, meaning that the order of the objects being combined does not affect the result. It also has a neutral element (such as the empty set or the trivial group) and an inverse element for each object.

How is the direct product related to other mathematical operations?

The direct product is related to other operations such as the Cartesian product, tensor product, and direct sum. It can also be seen as a generalization of the Cartesian product, where the resulting object contains elements of a higher dimension.

What are some applications of the direct product in science and engineering?

The direct product is commonly used in fields such as physics, computer science, and engineering to model and solve problems involving multiple interacting systems. It can also be used to represent complex data structures and relationships between objects.

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