Struggling with Linear Algebraic Groups? Need help finding simple examples?

In summary, the conversation is about someone trying to learn about Linear Algebraic Groups and finding the book by James Humpreys difficult for beginners. They are looking for sources with simple examples and worked-out problems, specifically in Humpreys' book or a similar text. They apologize for posting a lot of questions and express the belief that once they overcome the initial difficulties, they will be able to progress faster on their own. A suggestion is made for them to check out a book by T.A. Springer.
  • #1
esisk
44
0
Hi All,
I am trying to learn about Linear Algebraic Groups. I am using the book by James Humpreys. I love the subject, but I find it a bit, say, not so beginner-friendly. My goal is not being spoon-fed, but I am very interested in finding a source(s) whereby one is able to go through some concrete, simple examples. Ideally I am looking for some worked-out problems in James Humpreys' book or a similar text so I can get a start. Could you provide any help or suggestions? I just did not want post one question after the other as I am difficulty solving quite a few. I also have this conviction that if I were to jump over this initial hump, then I could proceed a bit faster on my own. I thank you for your time and apologize for the rambling.
 
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  • #2
You might find the book by T.A. Springer interesting.
 
  • #3
Thank you, I will try to get a hold of it.
 

Related to Struggling with Linear Algebraic Groups? Need help finding simple examples?

1. What is a linear algebraic group?

A linear algebraic group is a group of matrices that can be characterized by polynomial equations. In other words, it is a group of matrices that can be defined and manipulated using algebraic methods.

2. What are some examples of linear algebraic groups?

Some examples of linear algebraic groups include the general linear group, special linear group, orthogonal group, and symplectic group. These are all groups consisting of matrices with certain properties, such as invertibility or orthogonality.

3. How are linear algebraic groups different from other types of groups?

Linear algebraic groups are different from other types of groups in that they are defined using algebraic methods and properties. This means that they can be studied and manipulated using techniques from algebra, rather than purely geometric or analytic methods.

4. What are the applications of linear algebraic groups?

Linear algebraic groups have many applications in mathematics, physics, and engineering. They are used to study geometric objects, analyze data, and solve systems of equations. They also have applications in coding theory, cryptography, and other areas of computer science.

5. Are there any open problems related to linear algebraic groups?

Yes, there are several open problems related to linear algebraic groups. Some of these include finding efficient algorithms for computing with linear algebraic groups, classifying specific types of linear algebraic groups, and studying the representations of linear algebraic groups. Additionally, there are ongoing research efforts to apply linear algebraic groups to new areas and problems.

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