diff --git a/README.md b/README.md
index 65f2b6968..dbf7edbb2 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,8 @@ Please also consider citing the reference paper for the ProxDDP algorithm:
 * [Ludovic De Matteïs](https://github.com/LudovicDeMatteis) (LAAS-CNRS/Inria): feature developer
 * [Ewen Dantec](https://edantec.github.io/) (Inria): feature developer
 * [Antoine Bussy](https://github.com/antoine-bussy) (Aldebaran)
-* [Valentin Tordjman--Levavasseur](https://github.com/Tordjx) (Inria): feature developper
+* [Valentin Tordjman--Levavasseur](https://github.com/Tordjx) (Inria): feature developer
+* [Yann de Mont-Marin](https://github.com/ymontmarin) (Inria): Lie group formalism and associated features
 
 ## Acknowledgments
 
diff --git a/include/aligator/core/lie-algebra.hpp b/include/aligator/core/lie-algebra.hpp
new file mode 100644
index 000000000..a6a4b0480
--- /dev/null
+++ b/include/aligator/core/lie-algebra.hpp
@@ -0,0 +1,16 @@
+/// @file
+/// @copyright Copyright (C) 2025 INRIA
+#pragma once
+
+#include "aligator/fwd.hpp"
+
+namespace aligator {
+
+template <typename Derived> struct LieAlgebraTraits;
+
+/// @brief Base CRTP for Lie algebras.
+template <typename Derived> struct LieAlgebraBase {
+  using Traits = LieAlgebraTraits<Derived>;
+};
+
+} // namespace aligator
diff --git a/include/aligator/core/lie-group-base.hpp b/include/aligator/core/lie-group-base.hpp
new file mode 100644
index 000000000..78c97410d
--- /dev/null
+++ b/include/aligator/core/lie-group-base.hpp
@@ -0,0 +1,35 @@
+/// @file
+/// @copyright Copyright (C) 2025 INRIA
+#pragma once
+
+#include "aligator/fwd.hpp"
+
+namespace aligator {
+
+/// @brief Type traits for a Lie group. Usually required are the Lie group
+/// dimension, corresponding Lie Algebra, etc.
+template <typename Derived> struct LieGroupTraits {
+  using Scalar = typename Derived::Scalar;
+  static constexpr int Dim = Derived::Dim;
+};
+
+#define ALIGATOR_LIEGROUP_TRAITS_DEFINE(Traits)                                \
+  using Scalar = typename Traits::Derived;                                     \
+  static constexpr int Dim = Traits::Dim;                                      \
+  using LieAlgebraType = typename Traits::LieAlgebraType;                      \
+  using DualLieAlgebraType = typename Traits::DualLieAlgebraType
+
+template <typename Derived> struct LieGroupBase {
+  using Traits = LieGroupTraits<Derived>;
+  ALIGATOR_LIEGROUP_TRAITS_DEFINE(Traits);
+
+  Derived &derived() { return static_cast<Derived &>(*this); }
+
+  const Derived &derived() const { return static_cast<const Derived &>(*this); }
+
+  Derived &const_cast_derived() const {
+    return const_cast<Derived &>(derived());
+  }
+};
+
+} // namespace aligator