List all of the exterior algebra operations. Give me only their names and equations, and do so concisely and briefly, please.

Here are the main operations in an exterior algebra:

1. **Exterior (Wedge) Product**  
   \( A \wedge B \)

2. **Interior (Contraction) Product**  
   \( \iota_v(A) \)

3. **Exterior Derivative**  
   \( dA \)

4. **Hodge Star**  
   \( \star A \)

5. **Clifford Product (in Clifford Algebras)**  
   \( A \cdot B \)

These operations are fundamental to the structure and applications of exterior algebras.

Would you like further details or examples of these operations? Here are 5 follow-up questions:

1. How does the wedge product differ from the interior product?
2. What is the geometric significance of the Hodge star operation?
3. Can the exterior derivative be applied in any dimension?
4. How does the Clifford product extend the exterior algebra?
5. What are the applications of these operations in physics?

**Tip**: Familiarize yourself with the geometric interpretations of these operations, as they often provide deeper insights into their algebraic properties.

Discover the main operations in exterior algebra including the wedge product, interior product, exterior derivative, Hodge star, and Clifford product. Learn their names and equations with concise explanations.

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